tag:blogger.com,1999:blog-81073560438411469652024-03-19T16:59:06.942+07:00Charming MathCharming karena kelompok kita terdiri dari wanita-wanita yang memiliki pesona luar biasa. Suatu inner beauty yang senantiasa terpancar di setiap saat. Hal ini menginspirasi kami untuk mengabadikannya menjadi sebuah nama yang indah dan senantiasa terkenang dalam blog ini.the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-8107356043841146965.post-70278413181383014212009-12-14T11:44:00.011+07:002009-12-20T21:14:30.375+07:00TUGAS GEODAS II<meta equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 12"><meta name="Originator" content="Microsoft Word 12"><link style="font-family: arial;" rel="File-List" href="file:///C:%5CDOCUME%7E1%5CAWAN_O%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><link style="font-family: arial;" rel="Edit-Time-Data" href="file:///C:%5CDOCUME%7E1%5CAWAN_O%7E1%5CLOCALS%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_editdata.mso"><!--[if !mso]> <style> v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* 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22.5pt; text-align: justify; text-indent: -22.5pt; line-height: 150%; font-family: arial;font-family:arial;"><!--[if !supportLists]--><b style=""><span style="line-height: 150%;font-size:17pt;" ><span style="">7-1</span></span></b><b style=""><span style="line-height: 150%;font-size:17pt;" ><span style=""><span style="font-size:7pt;"> </span></span></span></b><!--[endif]--><b style=""><span style="line-height: 150%;font-size:17pt;" >Teorema Pythagoras</span></b><b style=""><span style="line-height: 150%;font-size:21pt;" ><o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><o:p> </o:p></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><span style=""> </span><span style="" lang="SV">Salah satu teor</span><span style="" lang="SV">ema yang paling terkenal dan paling berguna dalam bidang Geom</span><span style="" lang="SV">etri adalah Teorema Pythagoras. </span>Diberi nama setelah <span style="" lang="SV">ahli matematika </span><span style="" lang="SV">Yunani, Pythagoras.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><span style="" lang="SV"><span style=""> </span>Teorema ini menyatakan ba</span><span style="" lang="SV">hwa luas d</span><span style="" lang="SV">aerah di atas sisi hipotenus dari segitiga siku-siku sama dengan jumlah dari luas daerah di atas kaki-kaki d</span><span style="" lang="SV">ari segitiga tersebut.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><!--[if gte vml 1]><v:group id="_x0000_s1026" editas="canvas" style="'position:absolute;left:0;" coordorigin="438,5993" coordsize="7855,2658"> <o:lock ext="edit" aspectratio="t"> <v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_s1027" type="#_x0000_t75" style="'position:absolute;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]--><!--[endif]--><span style="" lang="SV"><span style=""> </span>Pada contoh 1-3, temukan cara untuk menghitung bagian terkecil persegi untuk menunjukkan bahwa luas </span><span style="" lang="SV">daerah persegi <i style="">A </i>dan <i style="">B</i> sama dengan luas daerah dari</span><span style="" lang="SV"> persegi <i style="">C</i> pada sisi miring.</span></p><p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><span style="font-weight: bold; font-style: italic;">Gambar bisa dilihat di makalah.</span></p><p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><span style="font-weight: bold; font-style: italic;">
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to="4777,9217"> </v:group></v:group><![endif]--><!--[if !vml]--><!--[endif]--><b style=""><span style="" lang="SV">Teorema Pythagoras<span style=""> </span>:</span></b><span style="" lang="SV"> Jika Δ ABC adalah segitiga siku-siku, maka kuadrat dari panjang sisi miring sama dengan jumlah kuadrat dari panjang kedua sisinya.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><b style=""><span style=""> </span><o:p></o:p></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><b style="">BUKTI</b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><b style=""><span style="" lang="SV">Diberikan</span></b><span style="" lang="SV"> <span style=""> </span><b style="">:</b> Segitiga siku-siku AC</span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFO0uh8sFXT-KZXEe6fX979Z0TkCUh4s4l_UVkIw_Y8HEcvWNE8AId4UzwhG-7Bxrv5F3bQv-t9Qlycv_kAaJDrm9gZ0VasJPY3WGi5HjAyoLnlzaggl2wqX1CucCXQWEuJSj70oMuwI6_/s1600-h/175px-Rtriangle.svg.png"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 175px; height: 149px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFO0uh8sFXT-KZXEe6fX979Z0TkCUh4s4l_UVkIw_Y8HEcvWNE8AId4UzwhG-7Bxrv5F3bQv-t9Qlycv_kAaJDrm9gZ0VasJPY3WGi5HjAyoLnlzaggl2wqX1CucCXQWEuJSj70oMuwI6_/s320/175px-Rtriangle.svg.png" alt="" id="BLOGGER_PHOTO_ID_5414951374296546226" border="0" /></a><span style="" lang="SV">B dengan panjang hipotenuse <i style="">c </i>dan panjang <span style=""> </span><span style=""> </span>ka</span><span style="" lang="SV">ki - kakinya <i style=""><span style=""> </span>a </i></span><span style="" lang="SV">dan <i style="">b.</i></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><b style=""><span style="" lang="IT">Buktikan</span></b><span style="" lang="IT"> <span style=""> </span><b style="">:</b><span style=""> </span></span>c²<span style="" lang="IT"> = </span>a²<span style="" lang="IT"> +<i style=""> </i></span>b²</p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><b style=""><span style="" lang="IT">Analisis<span style=""> </span></span></b><span style="" lang="IT"><span style=""> </span><span style=""> </span><b style="">: </b>Buatlah persegi di atas </span><span style="" lang="SV">Δ</span><span style="" lang="IT"> ABC seperti contoh di </span><span style="" lang="IT">atas. Persegi di atas <i style="">a</i> mempunyai luas </span>a²<span style="" lang="IT">. Persegi di atas <i style="">b</i> mempunyai luas </span>b²<span style="" lang="IT">. P</span><span style="" lang="IT">ersegi di atas <i style="">c </i>mempunyai luas </span>c²<span style="" lang="IT">. 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mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} </style> <![endif]--><span style=";font-size:100%;" lang="IT" >Gambar di atas menunjukan bahwa panjang sisi dari persegi kecil adalah <i style="">a – b.</i> Kita dapat mengetahui luas persegi besar dengan menambahk</span><span style=";font-size:100%;" lang="IT" >an luas dari ke empat segitiga dan lu</span><span style=";font-size:100%;" lang="IT" >as persegi kecil. 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Luas persegi ad</span><span style=";font-size:100%;" lang="IT" >alah (<i style="">a – b</i>)².</span>
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font-family:"Times New Roman","serif";} </style> <![endif]--><span style="font-family: arial;font-family:arial;" lang="IT"><o:p></o:p></span> <span style="font-weight: bold; font-style: italic; font-family: arial;font-family:arial;" >Gambar bisa dilihat di makalah.</span>
<br /><span style="font-weight: bold; font-style: italic; font-family: arial;font-family:arial;" >
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style="line-height: 150%;font-size:13pt;" lang="IT" >Teor</span></b><b style=""><span style="line-height: 150%;font-size:13pt;" lang="IT" >em</span></b><b style=""><span style="line-height: 150%;font-size:13pt;" lang="IT" >a 7-2<span style="position: relative; top: 5pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:9pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1090963060"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:arial;"><span style="" lang="IT">Jika </span><span style="" lang="SV">Δ</span><span style="" lang="IT"> ABC mempunyai sisi <i style="">a, b, </i>dan <i style="">c</i> dan </span>c²<span style="" lang="IT"> = </span>a²<span style="" lang="IT"> +</span><span style="" lang="IT"><i style=""> </i></span>b²<span style="" lang="IT"> , maka </span><span style="" lang="SV">Δ</span><span style="" lang="IT"> ABC adalah segitiga siku-siku.</span><a onblur="try 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mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} </style> <![endif]--><span style="font-family: arial;font-family:";font-size:100%;" lang="SV" >Δ ABC</span><span style="font-family: arial;font-family:";font-size:100%;" lang="SV" > adalah segitiga siku-s</span><span style="font-family: arial;font-family:";font-size:100%;" lang="SV" >iku , karena</span><p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;"><span lang="SV" style="font-size:100%;"><o:p> </o:p></span></p> <p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;"><span 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=<span style=""> </span>8</span></p><p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;">
<br /></p><p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;">
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<br /></p> <p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><span style=""> </span><i style=""><o:p></o:p></i></span></p> <p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="margin-left: 22.5pt; text-align: justify; text-indent: -22.5pt; line-height: 150%; font-family: arial;font-family:arial;"><!--[if !supportLists]--><span style="font-size:130%;"><b style=""><span style="line-height: 150%;" lang="IT"><span style="">7-2<span style=""> </span></span></span></b></span><!--[endif]--><b style=""><span style="line-height: 150%;font-size:17pt;" lang="IT" ><span style="font-size:130%;">Segi</span></span></b><b style=""><span style="line-height: 150%;font-size:17pt;" lang="IT" ><span style="font-size:130%;">tiga – Segitiga Isti</span></span></b><b style=""><span style="line-height: 150%;font-size:17pt;" lang="IT" ><span style="font-size:130%;">mewa</span></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1032" editas="canvas" style="'position:absolute;left:0;" coordorigin="765,5993" coordsize="3382,3821"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1033" type="#_x0000_t75" style="'position:absolute;left:765;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]-->
<br /><!--[endif]--><span style="" lang="IT"><o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span lang="SV" style="font-size:100%;">Gambar da</span><span lang="SV" style="font-size:100%;">n</span><span style="" lang="SV"><span style="font-size:100%;"> tabel disebelah kanan menunjukan dimensi dan spesifikasi untuk 2 macam sekrup mesin yang berbeda.</span><o:p style="font-family: arial;"></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;font-family:times new roman;"><span style="" lang="SV">Dimensi yang ber</span><span style="" lang="SV">tanda F menjelaskan ukuran kunci sekrup yang dibutuhkan untuk sekrup. Bagaimana dimensi </span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><span style="font-family: arial;font-family:times new roman;" >G dapat dihitung? Pengetahuan dari sudut-sudut 45º -45º -90º dan 30º -60º -90º dalam segitiga akan membantu perhitungan ini.</span><o:p></o:p></span></p>
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font-family:"Times New Roman","serif";} </style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults ext="edit" spidmax="1040"> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout ext="edit"> <o:idmap ext="edit" data="1"> </o:shapelayout></xml><![endif]--> <p class="MsoNormal" style="text-align: justify; line-height: 150%;font-family:arial;"><b style=""><span style="line-height: 150%;font-size:13pt;" lang="SV" >Teo</span></b><b style=""><span style="line-height: 150%;font-size:13pt;" lang="SV" >rema</span></b><b style=""><span style="line-height: 150%;font-size:13pt;" lang="SV" > 7-3</span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:13pt;" lang="SV" > <o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Panjang sisi miring dari segitiga yang mempunyai sudut 45º , 45º, 90º adalah <span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:18.75pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1090964073"> </o:OLEObject> </xml><![endif]--><span style="position: relative; top: 5pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:9pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1090964074"> </o:OLEObject> </xml><![endif]--></span>√2 <span style="" lang="IT">kali panjang kakinya.</span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1026" editas="canvas" style="'position:absolute;left:0;" coordorigin="2827,3838" coordsize="1800,1697"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1027" 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connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:group id="_x0000_s1034" style="'position:absolute;left:2337;top:6660;" coordorigin="2927,4095" coordsize="1050,1080"> <v:group id="_x0000_s1035" style="'position:absolute;left:2927;top:4095;" coordorigin="3127,4301" coordsize="1050,1080"> <v:line id="_x0000_s1036" style="'position:absolute'" from="3127,4301" to="4177,5381"> <v:line id="_x0000_s1037" style="'position:absolute'" from="3127,4301" to="3127,5381"> <v:line id="_x0000_s1038" style="'position:absolute;flip:x'" from="3127,5381" to="4177,5381"> </v:group><v:rect id="_x0000_s1039" style="'position:absolute;left:2927;top:5021;"> </v:group></v:group><![endif]--><!--[if !vml]-->
<br /></p><i style="font-family:arial;"><span style="" lang="IT"><span style="position: relative; top: 3pt;"><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1033" drawaspect="Content" objectid="_1090964081"> </o:OLEObject> </xml><![endif]--></span><o:p></o:p></i><a style="font-family: arial;" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8Uta3dw8CPoV72qv9iHepPjGQzr07-lROtCPtxsbBStkg78KxwE6xo1RvUVaA0ng_31Owkp2_EjQirs5D7VEsEp7cgXwQEt7sLrcn-0ogeI-XukJq6OA20Athq5tPXA2mXdlxbyxaSuu4/s1600-h/3.jpg"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 125px; height: 138px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8Uta3dw8CPoV72qv9iHepPjGQzr07-lROtCPtxsbBStkg78KxwE6xo1RvUVaA0ng_31Owkp2_EjQirs5D7VEsEp7cgXwQEt7sLrcn-0ogeI-XukJq6OA20Athq5tPXA2mXdlxbyxaSuu4/s320/3.jpg" alt="" id="BLOGGER_PHOTO_ID_5414960258741339666" border="0" /></a><span style="font-family:arial;">(AB)² = x² + x²</span>
<br />
<br /><span style="font-family:arial;">≡ (AB)² = 2x²</span>
<br />
<br /><span style="font-family:arial;">≡ (AB) = √</span><span style="font-family:arial;">2x²</span>
<br />
<br /><span style="font-family:arial;">≡ (AB) = x√2</span>
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<br />
<br />
<br />
<br />
<br /><span style="font-family: arial;font-family:arial;" >Contoh 1:</span>
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<br /><a style="font-family: arial;" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpqwXS93KNZcbu6UTstQpa2RZt0WSkG-x08g5HFnq4HNjoZLTGTmwZr6j5VkMSWGxb7WPNAieDjVFHaj8UtrMJO2TGgSuv3coh8YrfvgFHB0ms2o2QAq1ORXKdsUJAda6zxETpNguHKscE/s1600-h/h8.jpg"><img style="cursor: pointer; width: 96px; height: 121px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpqwXS93KNZcbu6UTstQpa2RZt0WSkG-x08g5HFnq4HNjoZLTGTmwZr6j5VkMSWGxb7WPNAieDjVFHaj8UtrMJO2TGgSuv3coh8YrfvgFHB0ms2o2QAq1ORXKdsUJAda6zxETpNguHKscE/s320/h8.jpg" alt="" id="BLOGGER_PHOTO_ID_5414962453558325602" border="0" /></a>
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<br /><span style="font-family: arial;font-family:arial;font-size:85%;" >1. ∠B dan</span><span style="font-family: arial;font-family:arial;" > ∠C</span><span style="font-family: arial;"> harus </span><span style="font-family: arial;" lang="SV">45º</span>
<br /><span style="font-family: arial;">2. </span><span style="font-family: arial;" lang="SV">Dengan menggunakan Teorema 7-3, </span><i style="font-family: arial;"><span style="" lang="IT">x<span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:18.75pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1090965238"> </o:OLEObject> </xml><![endif]--></span></i><span style="font-family: arial;font-family:arial;" >√2</span><i style="font-family: arial;"><span style="" lang="IT">=</span></i><span style="font-family: arial;" lang="IT"> 12
<br />
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mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} </style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults ext="edit" spidmax="2050"> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout ext="edit"> <o:idmap ext="edit" data="1"> </o:shapelayout></xml><![endif]--> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:13pt;" lang="IT" >Teore</span></b><b style=""><span style="line-height: 150%;font-size:13pt;" lang="IT" >ma 7-4<o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT">Panjang dari sisi dari segitiga siku-siku yang lebih panjang dari segitiga dengan sudut 30º, 60º, 90º adalah </span>√3 / 2<span style="" lang="IT"> </span><span style="" lang="SV"><span style="position: relative; top: 12pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:20.25pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1090965729"> </o:OLEObject> </xml><![endif]--></span><span style="" lang="IT"><span style=""> </span>kali panjang dari sisi miringnya atau </span><span style="" lang="SV"><span style="position: relative; top: 4pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1090965730"> </o:OLEObject> </xml><![endif]--></span><span style="" lang="IT"><span style=""> </span></span>√3 <span style="" lang="IT">kali panjang sisi yang lebih pendek.<o:p></o:p></span></p> <p class="MsoNormal" face="arial" style="text-align: justify; line-height: 150%; font-family: arial;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBTJVsBevGfO2lytcrY1wlGDjSa7Tw0Qrdc7vlrUi0XnwjNFSURsQxRjZ7PykG66KVaHRu5WDbUWWvpbSqnU8CfVgcbLlYbRQQqc25qM77dFxrczYVnnJmNoxHsb4isiR0oJIZTTMcKX3d/s1600-h/segitiga2.jpg"><img style="cursor: pointer; width: 193px; height: 173px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBTJVsBevGfO2lytcrY1wlGDjSa7Tw0Qrdc7vlrUi0XnwjNFSURsQxRjZ7PykG66KVaHRu5WDbUWWvpbSqnU8CfVgcbLlYbRQQqc25qM77dFxrczYVnnJmNoxHsb4isiR0oJIZTTMcKX3d/s320/segitiga2.jpg" alt="" id="BLOGGER_PHOTO_ID_5417313933478829538" border="0" /></a></p><span style="font-family: arial;"> a</span><span style="font-family: arial;font-family:arial;" >² = (BD)</span><span style="font-family: arial;font-family:arial;" >² + (1/2 a)</span><span style="font-family: arial;font-family:arial;" >²
<br />
<br />(BD)</span><span style="font-family: arial;font-family:arial;" >² = a</span><span style="font-family: arial;font-family:arial;" >² - a</span><span style="font-family: arial;font-family:arial;" >²/4 = a</span><span style="font-family: arial;font-family:arial;" >² (1 - 1/4)
<br />
<br />BD =</span><span style="font-family: arial;" lang="SV"><span style="position: relative; top: 4pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1090965730"> </o:OLEObject> </xml><![endif]--></span><span style="font-family: arial;" lang="IT"><span style=""> </span></span><span style="font-family: arial;font-family:arial;" >√</span><span style="font-family: arial;font-family:arial;" > 3/4 a = </span><span style="font-family: arial;" lang="SV"><span style="position: relative; top: 4pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1090965730"> </o:OLEObject> </xml><![endif]--></span><span style="font-family: arial;" lang="IT"><span style=""> </span></span><span style="font-family: arial;font-family:arial;" >(√3). (a/2 </span><span style="font-family: arial;font-family:arial;" >)
<br /></span>
<br /><span style="font-family: arial;" lang="SV"><o:p></o:p></span><i style="font-family: arial;"><span style="" lang="SV"><span style="position: relative; top: 14pt;"><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1034" drawaspect="Content" objectid="_1090965738"> </o:OLEObject> </xml><![endif]--></span></i><i style="font-family: arial;"><span style="" lang="IT"><o:p></o:p></span></i> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style=""><span style="" lang="IT"><o:p> </o:p></span></i></p><span style="font-family: arial;">BD = </span><span style="font-family: arial;font-family:arial;" > </span><span style="font-family: arial;" lang="SV"><span style="position: relative; top: 4pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:18pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1090965730"> </o:OLEObject> </xml><![endif]--></span><span style="font-family: arial;" lang="IT"><span style=""> </span></span><span style="font-family: arial;font-family:arial;" >√3 / 2 ( a</span><span style="font-family: arial;">)</span>
<br />
<br /><p class="MsoNormal" style="margin-left: 22.5pt; text-align: justify; text-indent: -22.5pt; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><b style=""><span style="line-height: 150%;font-size:17pt;" lang="SV" ><span style="">7-3<span style=";font-size:7pt;" > </span></span></span></b><!--[endif]--><b style=""><span style="line-height: 150%;font-size:17pt;" lang="IT" >Teorema Kekonkurenan Dalam Segitiga</span></b><b style=""><span style="line-height: 150%;font-size:17pt;" lang="SV" ><o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1127" editas="canvas" style="'position:absolute;left:0;" coordorigin="765,5993" coordsize="3382,3865"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1128" type="#_x0000_t75" style="'position:absolute;left:765;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]--><img src="file:///C:/DOCUME%7E1/AWAN_O%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image038.gif" shapes="_x0000_s1127 _x0000_s1128" align="left" width="248" height="279" /><!--[endif]--><b style=""><span style="line-height: 150%;font-size:14pt;" lang="SV" ><o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><span style=""> </span>Sebuah pabrik menghasilkan sebuah produk yang utamanya terjual di 3 kota</span><span style="" lang="SV"> besar. Sebuah pabrik baru yang terletak pada jarak yang sama dari masing-masing 3 kota. Bagaiman lokasi pabrik baru tersebut dapat ditemukan?<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Penjelasan dibawah ini menjawab pertanyaan tersebut.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Buatlah garis tegak yang membagi dua sisi sisi dari sebuah segitiga.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1129" editas="canvas" style="'position:absolute;left:0;" coordorigin="2185,10816" coordsize="3600,6043"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1130" type="#_x0000_t75" style="'position:absolute;left:2185;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]--><img src="file:///C:/DOCUME%7E1/AWAN_O%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image039.gif" shapes="_x0000_s1129 _x0000_s1130" align="left" width="276" height="454" /><!--[endif]--><span style="" lang="SV"><o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Bagai</span><span style="" lang="SV">mana perbandingan OA, OB, dan OC ? <o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Bagaimana perbandingan OD, OE, dan OF ? <o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Bagaimana perbandingan OG, OH, dan OI ? <o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:13pt;" lang="SV" >Teorema 7-5<o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><span style=""> </span>Garis bagi yang tegak lurus dari sisi sebuah segitiga berpotongan pada titik O yang berjarak sama dari ke tiga titik sudut segitiga.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="" lang="SV">BUKTI<o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="" lang="SV">Diberikan<span style=""> </span>:</span></b><span style="" lang="SV"> Δ ABC dengan </span><span style="" lang="SV">garis bagi yang tegak lurus <span style="font-style: italic;">l,l'</span> <span style="position: relative; top: 5pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style="'width:21.75pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image040.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1044" drawaspect="Content" objectid="_1090965748"> </o:OLEObject> </xml><![endif]-->dan <i style="">l”</i>.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="" lang="SV">Buktikan<span style=""> </span>:</span></b><span style="" lang="SV"> <span style="position: relative; top: 5pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" style="'width:21.75pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image042.wmz" title=""> </v:shape><![endif]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1045" drawaspect="Content" objectid="_1090965749"> </o:OLEObject> </xml><![endif]--><span style="font-style: italic;">l,l' </span>dan <i style="">l” </i><span style=""> </span>adalah melalui satu titik pada titik O dan bahwa <o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1045" editas="canvas" style="'position:absolute;left:0;" coordorigin="2527,5205" coordsize="4650,2623"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1046" type="#_x0000_t75" style="'position:absolute;left:2527;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:group id="_x0000_s1047" style="'position:absolute;left:3727;top:5822;" coordorigin="3727,5822" coordsize="2250,1236"> <v:line id="_x0000_s1048" style="'position:absolute'" from="3727,7057" to="5977,7058"> <v:line id="_x0000_s1049" style="'position:absolute;flip:y'" from="3727,5822" to="4477,7057"> <v:line id="_x0000_s1050" style="'position:absolute'" from="4477,5822" to="5977,7057"> </v:group><v:line id="_x0000_s1051" style="'position:absolute'" from="3727,6285" to="5227,7211"> <v:stroke startarrow="classic" endarrow="classic"> </v:line><v:line id="_x0000_s1052" style="'position:absolute;flip:y'" from="4477,6285" to="5377,7211"> <v:stroke startarrow="classic" endarrow="classic"> </v:line><v:line id="_x0000_s1053" style="'position:absolute'" from="4777,6594" to="4778,7674"> <v:stroke startarrow="classic" endarrow="classic"> </v:line></v:group><![endif]--><!--[if !vml]--><!--[endif]--><span style="" lang="SV"><span style=""> </span><span style=""> </span><i style="">OA = OB = OC.</i></span></p><p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="font-weight: bold; font-style: italic;">Gambar bisa dilihat di makalah.
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<br /><span style="" lang="SV"><i style=""><o:p></o:p></i></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style=""><span style="" lang="SV"><span style=""> </span><o:p></o:p></span></i></p><i style="font-family: arial;"><span style="" lang="SV"><o:p></o:p></span></i> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style=""><span style="" lang="SV"><o:p> </o:p></span></i></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="" lang="SV">Pernyataan dan Alasan :<o:p></o:p></span></b></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">1.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">l<span style=""> </span></span></i><span style="" lang="SV">adalah garis bagi yang tegak lurus dari <span style="position: relative; top: 2pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1046" type="#_x0000_t75" style="'width:20.25pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image044.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1046" drawaspect="Content" objectid="_1090965750"> </o:OLEObject> </xml><![endif]-->AB. (Diketahui)<o:p></o:p></span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">2.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">l’<span style=""> </span></span></i><span style="" lang="SV">adalah garis bagi yang tegak lurus dari <span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75" style="'width:20.25pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image046.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1047" drawaspect="Content" objectid="_1090965751"> </o:OLEObject> </xml><![endif]-->BC. (Diketahui)<o:p></o:p></span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">3.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">l</span></i><span style="" lang="SV"> dan <i style=""><span style=""> </span>l’ </i><span style=""> </span>berpotongan</span></p><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><span style="" lang="SV"> pada titik O. (Jika AB <span style="position: relative; top: 2pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1048" type="#_x0000_t75" style="'width:20.25pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image044.wmz" title=""> </v:shape><![endif]--></span><i style="">║</i><span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1049" type="#_x0000_t75" style="'width:20.25pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image046.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1049" drawaspect="Content" objectid="_1090965753"> </o:OLEObject> </xml><![endif]-->BC , maka <i style="">l ║ <span style=""> </span>l’ </i>)<o:p></o:p></span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">4.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">OA = OB. </span></i><span style="" lang="SV">(Sebuah titik pada garis bagi yang tegak lurus adalah berjarak sama dari titik akhirnya.)<o:p></o:p></span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">5.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">OB = OC.</span></i><span style="" lang="SV">(Mengapa? Karena berdasarkan postulat SAS)<o:p></o:p></span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">6.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">OA = OC.</span></i><span style="" lang="SV">(Sifat transitif)</span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="SV"><span style="">7.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><i style=""><span style="" lang="SV">O </span></i><span style="" lang="SV"><span style=""> </span>adalah pada garis bagi yang tegak lurus dari AC <span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75" style="'width:21pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\AWAN_O~1\LOCALS~1\Temp\msohtmlclip1\01\clip_image048.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1050" drawaspect="Content" objectid="_1090965754"> </o:OLEObject> </xml><![endif]-->.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style=""><span style="" lang="SV"><span style=""> </span></span></i><span style="" lang="SV">(Sebuah titik berjarak sama dari dua titik<span style=""> </span>adalah terletak pada garis bagi yang tegak <span style=""> </span>lurus dari ruas garis yang ditentukan oleh titik tersebut) <o:p></o:p></span></p> <p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;"><!--[if !supportLists]--><span style="" lang="IT"><span style="">8.<span style=";font-size:7pt;" > </span></span></span><!--[endif]--><!--[if gte vml 1]><v:group id="_x0000_s1054" editas="canvas" style="'position:absolute;left:0;" coordorigin="2527,3590" coordsize="4629,1919"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1055" type="#_x0000_t75" style="'position:absolute;left:2527;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:group id="_x0000_s1056" style="'position:absolute;left:2977;top:3898;" coordorigin="2977,4053" coordsize="3000,1234"> <v:line id="_x0000_s1057" style="'position:absolute;flip:x'" from="2977,4053" to="4477,5286"> <v:line id="_x0000_s1058" style="'position:absolute'" from="2977,5286" to="5977,5287"> <v:line id="_x0000_s1059" style="'position:absolute'" from="4477,4053" to="5977,5286"> </v:group><v:line id="_x0000_s1060" style="'position:absolute'" from="4627,3898" to="4628,5286"> <v:stroke dashstyle="dash"> </v:line><v:line id="_x0000_s1061" style="'position:absolute'" from="3727,4669" to="6277,5286"> <v:stroke dashstyle="dash"> </v:line><v:line id="_x0000_s1062" style="'position:absolute;flip:x'" from="2977,4669" to="5527,5286"> <v:stroke dashstyle="dash"> </v:line><v:rect id="_x0000_s1063" style="'position:absolute;left:4629;top:5132;"> </v:group><![endif]--><!--[if !vml]--><!--[endif]--><i style=""><span style="" lang="IT">O</span></i><span style="" lang="IT"> terletak pada <i style="">l, l’, l” <span style=""> </span></i>dan <i style="">OA = OB = OC.<span style=""> </span></i>(Pernyataan 4-8)</span></p><p class="MsoNormal" style="margin-left: 0.25in; text-align: justify; text-indent: -0.25in; line-height: 150%; font-family: arial;">
<br /></p><span style="font-weight: bold; font-style: italic; font-family: arial;font-family:arial;" >Gambar bisa dilihat d</span><span style="font-weight: bold; font-style: italic; font-family: arial;font-family:arial;" >i makalah.
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<br /><i style="font-family: arial;"><span style="" lang="IT"><o:p></o:p></span></i> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:14pt;" lang="IT" >Teorema 7-6<o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT">Garis bagi sudut dari sudut pada sebuah segitiga adalah melalui satu titik yaitu pada titik <i style="">I </i>yang berjarak sama dari ke tiga sisi dari segitiga.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT"><span style=""> </span>Titik yang ditentukan oleh garis bagi yang tegak lurus (Teorema 7-5) dan garis bagi sudut (Teorema 7-6) adalah di tengah lingkaran yang</span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT"> mempunyai hubungan istimewa dengan segitiga. <o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1064" editas="canvas" style="'position:absolute;left:0;" coordorigin="2527,4713" coordsize="2850,2314"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1065" type="#_x0000_t75" style="'position:absolute;left:2527;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:group id="_x0000_s1066" style="'position:absolute;left:2827;top:4867;" coordorigin="2827,4867" coordsize="2250,2160"> <v:group id="_x0000_s1067" style="'position:absolute;left:3127;top:5176;" coordorigin="3127,5176" coordsize="1800,1851"> <v:oval id="_x0000_s1068" style="'position:absolute;left:3127;top:5176;" strokeweight="1.25pt"> <v:line id="_x0000_s1069" style="'position:absolute'" from="4027,6101" to="4027,7027"> <v:line id="_x0000_s1070" style="'position:absolute;flip:y'" from="4027,5484" to="4627,6101"> <v:line id="_x0000_s1071" style="'position:absolute;flip:x" from="3427,5638" to="4027,6101"> <v:line id="_x0000_s1072" style="'position:absolute;flip:x'" from="3127,6101" to="4027,6255"> <v:line id="_x0000_s1073" style="'position:absolute;flip:x'" from="3127,5176" to="3877,6255"> <v:line id="_x0000_s1074" style="'position:absolute'" from="3127,6255" to="4927,6255"> <v:line id="_x0000_s1075" style="'position:absolute'" from="3877,5176" to="4927,6255"> </v:group><v:shapetype id="_x0000_t202" coordsize="21600,21600" spt="202" path="m,l,21600r21600,l21600,xe"> <v:stroke joinstyle="miter"> <v:path gradientshapeok="t" connecttype="rect"> </v:shapetype><v:shape id="_x0000_s1076" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1076'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">C<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1077" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1077'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">O<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1078" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1078'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">A<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1079" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1079'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">B<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape></v:group><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]--><img src="file:///C:/DOCUME%7E1/AWAN_O%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image051.gif" shapes="_x0000_s1064 _x0000_s1065 _x0000_s1066 _x0000_s1067 _x0000_s1068 _x0000_s1069 _x0000_s1070 _x0000_s1071 _x0000_s1072 _x0000_s1073 _x0000_s1074 _x0000_s1075 _x0000_s1076 _x0000_s1077 _x0000_s1078 _x0000_s1079" align="left" width="228" height="181" /><!--[endif]--><span style="" lang="IT"><o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT"><span style=""> </span></span><span style="" lang="SV">Lingkaran <i style="">O</i> memuat tiga titik sudut<span style=""> </span>dari Δ ABC. Titik tengah adalah titik dari perpotongan garis bagi yang tegak lurus. Jari-jarinya adalah <i style="">OA</i>. Lingkaran <i style="">O </i>disebut<span style=""> </span><i style="">lingkaran yang membatasi.<o:p></o:p></i></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1081" editas="canvas" style="'position:absolute;left:0;" coordorigin="3127,10632" coordsize="2850,2092"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1082" type="#_x0000_t75" style="'position:absolute;left:3127;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:group id="_x0000_s1083" style="'position:absolute;left:3277;top:10987;" coordorigin="3277,10987" coordsize="2550,1388"> <v:line id="_x0000_s1084" style="'position:absolute;flip:x'" from="3277,10987" to="5227,12375" strokeweight="1.25pt"> <v:line id="_x0000_s1085" style="'position:absolute'" from="3277,12375" to="5827,12375" strokeweight="1.25pt"> <v:line id="_x0000_s1086" style="'position:absolute'" from="5227,10987" to="5827,12375" strokeweight="1.25pt"> <v:oval id="_x0000_s1087" style="'position:absolute;left:4477;top:11295;" strokeweight="1.25pt"> </v:group><v:group id="_x0000_s1088" style="'position:absolute;left:3277;top:10987;" coordorigin="3277,10987" coordsize="2550,1388"> <v:line id="_x0000_s1089" style="'position:absolute;flip:y'" from="4927,10987" to="5227,11912" strokeweight="1pt"> <v:line id="_x0000_s1090" style="'position:absolute;flip:y'" from="3277,11912" to="4927,12375"> <v:line id="_x0000_s1091" style="'position:absolute'" from="4927,11912" to="5827,12375"> </v:group><v:shape id="_x0000_s1092" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">T<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1093" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">R<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1094" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">S<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:line id="_x0000_s1095" style="'position:absolute'" from="4927,11866" to="4927,12328"> <v:shape id="_x0000_s1096" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">W<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1097" type="#_x0000_t202" style="'position:absolute;" filled="f" stroked="f"> <v:textbox> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><i style="'mso-bidi-font-style:normal'">I<o:p></o:p></i></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]--><img src="file:///C:/DOCUME%7E1/AWAN_O%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image052.gif" shapes="_x0000_s1081 _x0000_s1082 _x0000_s1083 _x0000_s1084 _x0000_s1085 _x0000_s1086 _x0000_s1087 _x0000_s1088 _x0000_s1089 _x0000_s1090 _x0000_s1091 _x0000_s1092 _x0000_s1093 _x0000_s1094 _x0000_s1095 _x0000_s1096 _x0000_s1097" align="left" width="230" height="165" /><!--[endif]--><!--[if gte vml 1]><v:line id="_x0000_s1080" style="'position:absolute;left:0;text-align:left;z-index:-9'" from="702pt,335.25pt" to="702pt,389.25pt"><![endif]--><!--[if !vml]--><span style="position: absolute; z-index: -9; left: 0px; margin-left: 935px; margin-top: 446px; width: 2px; height: 74px;"><img src="file:///C:/DOCUME%7E1/AWAN_O%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image053.gif" shapes="_x0000_s1080" width="2" height="74" /></span><!--[endif]--><span style="" lang="SV"><span style=""> </span><o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><span style=""> </span>Lingkaran <i style="">I </i><span style=""> </span>menyinggung setiap sisi </span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">dari Δ RST secara pasti pada satu titik. Titik tengah adalah titik dari perpotongan garis bagi sudut sebuah segitiga. Jari-jarinya adalah <i style="">IW</i>. Lingkaran <i style="">I</i><span style=""> </span>disebut <i style="">lingkaran yang dibatasi.<o:p></o:p></i></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style=""><span style="" lang="SV"><o:p> </o:p></span></i></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style=""><span style="" lang="SV"><span style=""> </span></span></i><span style="" lang="SV">Jika kamu menggambar sebuah segitiga dan ke tiga garis tingginya, kamu akan melihat bahwa garis yang berisikan garis tinggi adalah kongkuren (melalui satu titik).</span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><o:wrapblock pagebreak="t"> <v:group id="_x0000_s1098" editas="canvas" style="'position:absolute;left:0;" coordorigin="2527,3180" coordsize="2700,1448"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1099" type="#_x0000_t75" style="'position:absolute;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:line id="_x0000_s1100" style="'position:absolute;flip:x'" from="2827,3239" to="3277,4474"> <v:line id="_x0000_s1101" style="'position:absolute'" from="2827,4474" to="4477,4475"> <v:line id="_x0000_s1102" style="'position:absolute'" from="3277,3239" to="4477,4475"> <v:line id="_x0000_s1103" style="'position:absolute'" from="3277,3239" to="3278,4475"> <v:line id="_x0000_s1104" style="'position:absolute;flip:y'" from="2827,3548" to="3577,4474"> <v:line id="_x0000_s1105" style="'position:absolute'" from="3127,3856" to="4477,4474"> <v:rect id="_x0000_s1106" style="'position:absolute;left:3277;top:4319;"> </v:group><![endif]--><!--[if !vml]-->
<br /></p><p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju5l0t_5kpm_kTdqzg5YrlkCfQgVB0JiB8u-XU0at4Tcc5sXZhl10vt_-g9Cb_VLPhxSWDWnBrLA4BVAmKAHqSdEYbhywO6s8vrBT1PbsI1wLf-ImSMMeKYJ-Wktch6m8fsvM5nU_LVlOn/s1600-h/sgtg_sebarang.gif"><img style="cursor: pointer; width: 181px; height: 167px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju5l0t_5kpm_kTdqzg5YrlkCfQgVB0JiB8u-XU0at4Tcc5sXZhl10vt_-g9Cb_VLPhxSWDWnBrLA4BVAmKAHqSdEYbhywO6s8vrBT1PbsI1wLf-ImSMMeKYJ-Wktch6m8fsvM5nU_LVlOn/s320/sgtg_sebarang.gif" alt="" id="BLOGGER_PHOTO_ID_5417316563472384050" border="0" /></a></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[endif]--><!--[if gte vml 1]></o:wrapblock><![endif]--><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <span style="line-height: 150%; font-family: arial;font-family:";font-size:12pt;" lang="SV" >
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<br /><p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:14pt;" lang="SV" >Teorema 7-7<o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT"><span style=""> </span>Garis yang terdiri dari garis tinggi sebuah segitiga berpotongan pada sebuah titik.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="IT"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Untuk beberapa segitiga ada tiga ruas garis yang disebut garis tengah.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1107" editas="canvas" style="'position:absolute;left:0;" coordorigin="2527,3651" coordsize="3900,1915"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1108" type="#_x0000_t75" style="'position:absolute;left:2527;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:group id="_x0000_s1109" style="'position:absolute;left:2677;top:4422;" coordorigin="2677,4422" coordsize="900,772"> <v:line id="_x0000_s1110" style="'position:absolute;flip:x'" from="2677,4422" to="2977,5194"> <v:line id="_x0000_s1111" style="'position:absolute'" from="2677,5194" to="3577,5194"> <v:line id="_x0000_s1112" style="'position:absolute'" from="2977,4422" to="3577,5194"> </v:group><v:group id="_x0000_s1113" style="'position:absolute;left:4027;top:4422;" coordorigin="2677,4422" coordsize="900,772"> <v:line id="_x0000_s1114" style="'position:absolute;flip:x'" from="2677,4422" to="2977,5194"> <v:line id="_x0000_s1115" style="'position:absolute'" from="2677,5194" to="3577,5194"> <v:line id="_x0000_s1116" style="'position:absolute'" from="2977,4422" to="3577,5194"> </v:group><v:group id="_x0000_s1117" style="'position:absolute;left:5377;top:4422;" coordorigin="2677,4422" coordsize="900,772"> <v:line id="_x0000_s1118" style="'position:absolute;flip:x'" from="2677,4422" to="2977,5194"> <v:line id="_x0000_s1119" style="'position:absolute'" from="2677,5194" to="3577,5194"> <v:line id="_x0000_s1120" style="'position:absolute'" from="2977,4422" to="3577,5194"> </v:group><w:wrap type="square"> </v:group><![endif]--><!--[if !vml]--><img src="file:///C:/DOCUME%7E1/AWAN_O%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image055.gif" shapes="_x0000_s1107 _x0000_s1108 _x0000_s1109 _x0000_s1110 _x0000_s1111 _x0000_s1112 _x0000_s1113 _x0000_s1114 _x0000_s1115 _x0000_s1116 _x0000_s1117 _x0000_s1118 _x0000_s1119 _x0000_s1120" align="left" width="313" height="149" /><!--[endif]--><b style=""><span style="" lang="SV">Definisi 7-1</span></b><span style="" lang="SV"><o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Garis tengah dari sebuah segitiga adalah ruas garis yang menghubungkan sebuah titik puncak ke titik tengah dari sisi yang berlawanan.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><span style=""> </span>Jika kamu menggambar tiga garis tengah dari sebuah segitiga, kamu akan melihat bahwa ke tiga garis tengah juga kongkuren (melalui satu titik).<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1125" editas="canvas" style="'position:absolute;left:0;" coordorigin="1797,6481" coordsize="3600,1980"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1126" type="#_x0000_t75" style="'position:absolute;left:1797;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape></v:group><![endif]--><!--[if !vml]--><!--[endif]--><span style="" lang="SV"><span style=""> </span>Ada juga hubungan menarik lainnya.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><!--[if gte vml 1]><v:group id="_x0000_s1131" style="'position:absolute;left:0;text-align:left;" coordorigin="2337,6660" coordsize="2700,1621"> <v:line id="_x0000_s1132" style="'position:absolute'" from="2877,7561" to="5037,8281"> <v:line id="_x0000_s1133" style="'position:absolute;flip:y'" from="2337,7381" to="3957,8281"> <v:line id="_x0000_s1134" style="'position:absolute'" from="3237,6660" to="3417,8280"> </v:group><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte vml 1]><v:group id="_x0000_s1121" style="'position:absolute;left:0;text-align:left;" coordorigin="3727,5822" coordsize="2250,1236"> <v:line id="_x0000_s1122" style="'position:absolute'" from="3727,7057" to="5977,7058"> <v:line id="_x0000_s1123" style="'position:absolute;flip:y'" from="3727,5822" to="4477,7057"> <v:line id="_x0000_s1124" style="'position:absolute'" from="4477,5822" to="5977,7057"> </v:group><![endif]--><!--[if !vml]--><!--[endif]--><span style="" lang="SV"><span style=""> </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="font-weight: bold; font-style: italic;">Gambar bisa dilihat di makalah.
<br /></span>
<br /><i style=""><span style="" lang="SV"><o:p></o:p></span></i></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Bagaimana perbandingan <i style="">AG </i>dan <i style="">AX </i>?<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style="">AG : AX = 4 : 6 = 2 : 3<o:p></o:p></i></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;">Bagaimana perbandingan <i style="">BG </i>dan <i style="">BY </i>?</p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style="">BG : BY = 6 : 9 = 2 : 3<o:p></o:p></i></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;">Bagaimana perbandingan <i style="">CG </i>dan <i style="">CZ </i>?</p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><i style="">CG : CZ = 7 : 10,5 = 2 : 3<o:p></o:p></i></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><span style="" lang="SV">Teorema berikut ini dinyatakan tanpa bukti.<o:p></o:p></span></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:14pt;" lang="SV" ><o:p> </o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%; font-family: arial;"><b style=""><span style="line-height: 150%;font-size:14pt;" lang="SV" >Teorema 7-8<o:p></o:p></span></b></p> <p class="MsoNormal" style="text-align: justify; line-height: 150%;"><span style="" lang="SV"><span style="font-family: arial;"> </span><span style="font-family: arial;">Garis tengah pada sebuah segitiga berpotongan pada satu titik, sehingga dua per tiga dari masing-masing titik puncak ke sisi yang berlawanan.</span><o:p></o:p></span></p>
<br /><span lang="SV" style="font-family:arial;"><o:p></o:p></span><p style="font-family: arial;"></p> the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com0tag:blogger.com,1999:blog-8107356043841146965.post-46238265677341892462009-10-12T11:30:00.002+07:002009-10-12T11:50:52.922+07:00TUGAS 5 PDM<span style="font-weight: bold;">UNION<br /><br /></span>1. Show that (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)<br /> Proof:<br /><span style="font-weight: bold;"></span> i) Show that (A ∪ B) ∩ C ⊂ (A ∩ C) ∪ (B ∩ C)<br /> Take any x ∈ (A ∪ B) ∩ C<br /> Obvious x ∈ (A ∪ B) ∩ C<br /> ≡ x ∈ (A ∪ B) ∧ x ∈ C<br /> ≡ (x ∈ A ∨ x ∈ B) ∧ x ∈ C<br /> ≡ (x ∈ A ∧ x ∈ C) ∨ (x ∈ B ∧ x ∈ C)<br /> ≡ x ∈ (A ∩ C) ∪ x ∈ (B ∩ C)<br /> ≡ x ∈ (A ∩ C) ∪ (B ∩ C) .......1)<br /> We get for all x ∈ (A ∪ B) ∩ C then x ∈ (A ∩ C) ∪ (B ∩ C).<br /> It means (A ∪ B) ∩ C ⊂ (A ∩ C) ∪ (B ∩ C)<br /><br /> ii) Show that (A ∩ C) ∪ (B ∩ C) ⊂ (A ∪ B) ∩ C<br /> Take any x ∈ (A ∩ C) ∪ (B ∩ C)<br /> Obvious x ∈ (A ∩ C) ∪ (B ∩ C)<br /> ≡ x ∈ (A ∩ C) ∨ (B ∩ C)<br /> ≡ (x ∈ A ∧ x ∈ C) ∨ (x ∈ B ∧ x ∈ C)<br /> ≡ (x ∈ A ∧ x ∈ C) ∨ (x ∈ B ∧ x ∈ C)<br /> ≡ x ∈ C ∧ (x ∈ A ∨ x ∈ B) (Asso)<br /> ≡ (x ∈ A ∨ x ∈ B) ∧ x ∈ C<br /> ≡ x ∈ (A ∪ B) ∩ C .......2)<br /> From 1) and 2) we conclude that (A ∪ B) ∩ C is true.<br /> So, (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com0tag:blogger.com,1999:blog-8107356043841146965.post-40282810919340138202009-10-12T11:03:00.002+07:002009-10-12T11:28:44.507+07:00TUGAS 4 PDM2). b. Show that<br /> A ∩ B = B ∩ A<br /> Proof :<br /> (i) Show that A ∩ B ⊂ B ∩ A<br /> Take any x ∈ A ∩ B<br /> Obvious x ∈ A ∩ B<br /> ≡ x ∈ A ∧ x ∈ B<br /> ≡ x ∈ B ∧ x ∈ A (komutatif)<br /> ≡ x ∈ (B ∩ A)<br /> So, A ∩ B ⊂ B ∩ A .......(1)<br /><br /><br /> (ii) Show that B ∩ A ⊂ A ∩ B<br /> Take any x ∈ B ∩ A<br /> Obvious x ∈ B ∩ A<br /> ≡ x ∈ B ∧ x ∈ A<br /> ≡ x ∈ A ∧ x ∈ B (komutatif)<br /> ≡ x ∈ (A ∩ B)<br /> So, B ∩ A ⊂ A ∩ B .......(2)<br /><br /> So, from (1) and (2) we conclude that A ∩ B = B ∩ A<br /><br /> c. Show that<br /> (A ∩ B) ∩ C = A ∩ (B ∩ C)<br /> Proof :<br /> (i) Show that (A ∩ B) ∩ C ⊂ A ∩ (B ∩ C)<br /> Take any x ∈ (A ∩ B) ∩ C<br /> Obvious x ∈ (A ∩ B) ∩ C<br /> ≡ x ∈ A ∧ x ∈ B ∧ x ∈ C<br /> ≡ x ∈ A ∧ x ∈ (B ∧ C) (assosiatif)<br /> ≡ x ∈ A ∧ x ∈ (B ∩ C)<br /> So, (A ∩ B) ∩ C ⊂ A ∩ (B ∩ C)........ (1)<br /><br /> (ii) Show that (A ∩ B) ∩ C ⊂ A ∩ (B ∩ C)<br /> Take any x ∈ A ∩ (B ∩ C)<br /> Obvious x ∈ A ∩ (B ∩ C)<br /> ≡ x ∈ A ∧ x ∈ B x ∈ C<br /> ≡ x ∈ (A ∧ B) ∧ x ∈ C (assosiatif)<br /> ≡ x ∈ (A ∩ B) x ∈ C<br /> So, A ∩ (B ∩ C) ⊂ (A ∩ B) ∩ C ........ (2)<br /><br />So, from (1) and (2) we conclude that (A ∩ B) ∩ C = A ∩ (B ∩ C)the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com0tag:blogger.com,1999:blog-8107356043841146965.post-21579415579544906722009-09-30T09:46:00.006+07:002009-10-05T13:52:16.845+07:00TUGAS 3 PDM<span style="font-weight: bold;">BUKTI KESAHAN ARGUMEN<br /><br />1) Modus Ponens (MP)</span><br /> [(p → q) ∧ p] → q<br /> ≡ ∼[(∼p ∨ q) ∧ p] ∨ q (Imp)<br /> ≡ [(p ∧ ∼q) ∨ ∼p] ∨ q (Komp. DM)<br /> ≡ [(p ∨ ∼p) ∧ (∼p ∨ ∼q)] ∨ q (Dist)<br /> ≡ [T ∧ (∼p ∨ ∼q)] ∨ q (Komp)<br /> ≡ (∼p ∨ ∼q) ∨ q (Id)<br /> ≡ ∼p ∨ (∼q ∨ q) (Asso)<br /> ≡ ∼p ∨ T (Komp)<br /> ≡ T (Id)<br /><br /><br /><span style="font-weight: bold;">2) Modus Tolens (MT)</span><br /> [(p → q) ∧ ∼q] → ∼p<br /> ≡ [(∼p ∨ q) ∧ ∼q] → ∼p (Imp)<br /> ≡ (∼p ∧ ∼q) ∨ (q ∧ ∼q) → ∼p (Dist)<br /> ≡ (∼p ∧ ∼q) ∨ F → ∼p (Komp)<br /> ≡ (∼p ∧ ∼q) → ∼p (Id)<br /> ≡ ∼(∼p ∧ ∼q) ∨ ∼p (Imp)<br /> ≡ p ∨ q ∨ ∼p (DM)<br /> ≡ p ∨ (q ∨ ∼p) (Asso)<br /> ≡ p ∨ (∼p ∨ q) (Komu)<br /> ≡ (p ∨ ∼p) ∨ q (Asso)<br /> ≡ T ∨ q (Komp)<br /> ≡ T (Id)<br /><br /><span style="font-weight: bold;">3) Silogisme</span><br />[(p → q) ∧ (q → r)] → (p → r)<br /> ≡ (p → q) → [(q → r)→ (p → r)] (Eksp)<br /> ≡ (p → q) → [(∼q ∨ r)→ (∼p ∨ r)] (Imp)<br /> ≡ (p → q) → [(q ∧ ∼r) ∨ (∼p ∨ r)] (Imp)<br /> ≡ (p → q) → [(q ∧ ∼r) ∨ (r ∨ ∼p)] (Kom)<br /> ≡ (p → q) → [(q ∧ ∼r) ∨ r] ∨ ∼p (Asso)<br /> ≡ (p → q) → [(q ∨ r) ∧ (∼r ∨ r)] ∨ ∼p (Dist)<br /> ≡ (p → q) → [(q ∨ r) ∧ T] ∨ ∼p (Komp)<br /> ≡(p → q) → (q ∨ r) ∨ ∼p (Id)<br /> ≡(∼p ∨ q) → q ∨ r ∨ ∼p (Imp)<br /> ≡∼(∼p ∨ q) ∨ (q ∨ r ∨ ∼p) (Imp)<br /> ≡∼(∼p ∨ q) ∨ (∼p ∨ q ) ∨ r (Asso)<br /> ≡ T ∨ r (komp)<br /> ≡ T (id)<br /><br /><br /><span style="font-weight: bold;">4) Distruktif Silogisme (DS)</span><br /> (p ∨ q) ∧ ∼p → q<br /> ≡ (p ∧ ∼p) ∨ (q ∧ ∼p) → q (Dist)<br /> ≡ F ∨ (q ∧ ∼p) → q (Komp)<br /> ≡ (q ∧ ∼p) → q (Id)<br /> ≡ ∼(q ∧ ∼p) ∨ q (Imp)<br /> ≡ (∼q ∨ p) ∨ q (DM)<br /> ≡ ∼q ∨ (p ∨ q) (Komu)<br /> ≡ (∼q ∨ q) ∨ p (Asso)<br /> ≡ T ∨ p (Komp)<br /> ≡ T (Id)<br /><br /><span style="font-weight: bold;">5) Konstruktif Dilema (KD)</span><br />{[(p → q) ∧ (r → s)] ∧ (p ∨ r)} → (q ∨ s)<br /> ≡ [(∼p ∨ q) ∧ (∼r ∨ s)] ∧ (p ∨ r)} → (q ∨ s) (Imp)<br /> ≡ [(p ∧ ∼q) ∨ (r ∧ ∼s)] ∨ (∼p ∧ ∼r) ∨ (q ∨ s) (Imp)<br /> ≡ [(p ∧ ∼q) ∨ (∼p ∧ ∼r)] ∨ (r ∧ ∼s) ∨ (q ∨ s) (Asso)<br /> ≡ [(p ∧ ∼q) ∨ (∼p ∧ ∼r)] ∨ [(r ∧ ∼s) ∨ (q ∨ s)] (Asso)<br /> ≡ [{(p ∧ ∼q) ∨ ∼p }∧ {(p ∧∼q) ∨ ∼r}] ∨ [(r ∧ ∼s) ∨ (q ∨ s)] (Dist)<br /> ≡ [{(p ∧ ∼q) ∨ ∼p }∧ {(p ∧∼q) ∨ ∼r}] ∨ [{(r ∧ ∼s) ∨ s} ∨ q)] (Asso)<br /> ≡ [{(p ∨ ∼p) ∧ (∼q ∨ ∼p)}∧ {(p ∨∼r) ∧ (∼q ∨∼r)}] ∨[{(r ∨ s) ∧ (∼s ∨ s)} ∨ q] (Dist)<br /> ≡ [{T ∧ (∼q ∨ ∼p)}∧ {(p ∨∼r) ∧ (∼q ∨∼r)}] ∨[{(r ∨ s) ∧ T} ∨ q] (Komp)<br /> ≡ [{(∼q ∨ ∼p)}∧ {(p ∨∼r) ∧ (∼q ∨∼r)}] ∨[{(r ∨ s)} ∨ q] (Id)<br /> ≡ [{(∼q ∨ ∼p)}∧ {(p ∨∼r) ∧ (∼q ∨∼r)}∨ q] ∨ (r ∨ s) (Asso)<br /> ≡ [{(∼q ∨ ∼p)}∨ q} ∧ {(p ∨∼r) ∨ q} ∧ {(∼q ∨∼r)∨ q}] ∨ (r ∨ s) (Dist)<br /> ≡ [{(∼q ∨ q) ∨ ∼p} ∧ (p ∨ q) ∨ ∼r) ∧ {(∼q ∨ q) ∨ ∼r}] ∨ (r ∨ s) (Asso)<br /> ≡ [T ∨ ∼p ∧ (p ∨ q) ∨ ∼r) ∧ (T ∨ ∼r)] ∨ (r ∨ s) (Komp)<br /> ≡ [T ∧ (p ∨ q ∨ ∼r) ∧ T] ∨ (r ∨ s) (Id)<br /> ≡ (p ∨ q ∨ ∼r) ∨ (r ∨ s) (Id)<br /> ≡ (r ∨ ∼r) ∨ (p ∨ q ∨ s) (Asso)<br /> ≡ T ∨ (p ∨ q ∨ s) (Komp)<br /> ≡ T (Id)<br /><br /><span style="font-weight: bold;">6) Distruktif Dilema (DD)</span><br />{[(p → q) ∧ (r → s)] ∧ (∼q ∨ ∼s)} → (∼p ∨ ∼r )<br /> ≡ [(∼p ∨ q) ∧ (∼r ∨ s)] ∧ (∼q ∨ ∼s)] → (∼p ∨ ∼r ) (Imp)<br /> ≡ [(p ∧ ∼q) ∧ (r ∧∼s) ∨ (q ∧ s)] ∨ (∼p ∨ ∼r ) (Imp)<br /> ≡ [(p ∧ ∼q) ∧ (q ∧ s) ∨ (r ∧ ∼s) ∨ (∼p ∨ ∼r )] (Asso)<br /> ≡ [(p ∧ ∼q) ∧ (q ∧ s)] ∨ [(r ∧ ∼s) ∨ (∼p ∨ ∼r )] (Asso)<br /> ≡ [{(p ∧ ∼q) ∨ q} ∧ {(p ∧ ∼q) ∨ s)}] ∨ [(r ∧ ∼s) ∨ (∼p ∨ ∼r )] (Dist)<br /> ≡ [{(p ∧ ∼q) ∨ q} ∧ {(p ∧ ∼q) ∨ s)}] ∨ [{(r ∧ ∼s) ∨∼r}∨∼p] (Asso)<br /> ≡ [{(p ∨ q) ∧ (∼q ∨ q)} ∧ {(p ∨ s) ∧ (∼q ∨ s)}] ∨ [{(r ∨∼r) ∧ (∼s ∨∼r)}∨∼p] (Dist)<br /> ≡ [{(p ∨ q) ∧ T} ∧ {(p ∨ s) ∧ (∼q ∨ s)}] ∨ [{T ∧ (∼s ∨∼r)}∨∼p] (Komp)<br /> ≡ [(p ∨ q) ∧ (p ∨ s) ∧ (∼q ∨ s)] ∨ [(∼s ∨∼r) ∨∼p] (Id)<br /> ≡ [(p ∨ q) ∧ (p ∨ s) ∧ (∼q ∨ s) ∨ ∼p] ∨ (∼s ∨∼r) (Asso)<br /> ≡ [{(p ∨ q) ∨ ∼p} ∧ {(p ∨ s) ∨ ∼p} ∧ {(∼q ∨ s) ∨ ∼p}] ∨ (∼s ∨∼r) (Dist)<br /> ≡ [{(p ∨ ∼p) ∨ q} ∧ {(p ∨ ∼p)∨ s} ∧ (∼q ∨ s ∨∼p)] ∨ (∼s ∨∼r) (Asso)<br /> ≡ [(T ∨ q) ∧ (T∨ s) ∧ (∼q ∨ s ∨∼p)] ∨ (∼s ∨∼r) (Komp)<br /> ≡ [T ∧ T ∧ (∼q ∨ s ∨∼p)] ∨ (∼s ∨∼r) (Id)<br /> ≡ (∼q ∨ s ∨∼p) ∨ (∼s ∨∼r) (Id)<br /> ≡ ( s ∨∼s) ∨ (∼p ∨∼q ∨∼r) (Asso)<br /> ≡ T ∨ (∼p ∨∼q ∨∼r) (Komp)<br /> ≡ T (Id)the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com0tag:blogger.com,1999:blog-8107356043841146965.post-18848694492982786802009-09-15T10:37:00.004+07:002009-09-15T12:28:40.652+07:00TUGAS 2 PDM<span>1. Tentukan invers, konvers, dan kontraposisi dari proposisi berikut ini:
<br /></span><span style="font-weight: bold;">
<br /></span> 1) (p∧q)→r
<br /> Invers : ∼(p∧q)→∼r
<br /> ≡ (∼p∨∼q)→∼r
<br /> Konvers : r→(p∧q)
<br /> Kontraposisi : ∼r→∼(p∧q)
<br /> ≡ ∼r→(∼p∨∼q)
<br />
<br />2) p→(q∧r)
<br /> Invers : ∼p→∼(q∧r)
<br /> ≡ ∼p→(∼q∨∼r)
<br /> Konvers : (q∧r)→p
<br /> Kontraposisi : ∼(q∧r)→∼p
<br /> ≡ (∼q∨∼r)→∼p
<br />
<br />3) ∼p→(q∧∼r)
<br /> Invers : ∼(∼p)→∼(q∧∼r)
<br /> ≡ p→(∼q∨r)
<br /> Konvers : (q∧∼r)→∼p
<br /> Kontraposisi : ∼(q∧∼r)→∼(∼p)
<br /> ≡ (∼q∨r)→p
<br />
<br />4) (p∨∼q)→(q∧r)
<br /> Invers : ∼(p∨∼q)→∼(q∧r)
<br /> ≡ (∼p∧q)→(∼q∨∼r)
<br /> Konvers : (q∧r)→ (p∨∼q)
<br /> Kontraposisi : ∼(q∧r)→∼(p∨∼q)
<br /> ≡ (∼q∨∼r)→(∼p∧q)
<br />
<br />5) (∼q∧∼r)→(∼p∨q)
<br /> Invers : ∼(∼q∧∼r)→∼(∼p∨q)
<br /> ≡ (q∨r)→(p∧∼q)
<br /> Konvers : (∼p∨q)→ (∼q∧∼r)
<br /> Kontraposisi : ∼(∼p∨q)→∼(∼q∧∼r)
<br /> ≡ (p∧∼q)→(q∨r)
<br />
<br />6) (q∨∼r)→(p∧r)
<br /> Invers : ∼(q∨∼r)→∼(p∧r)
<br /> ≡ (∼q∧r)→(∼p∨∼r)
<br /> Konvers : (p∧r)→ (q∨∼r)
<br /> Kontraposisi : ∼(p∧r)→∼(q∨∼r)
<br /> ≡ (∼p∨∼r)→(∼q∧r)
<br />
<br />
<br />
<br /><span>2. Tentukan invers, konvers, dan kontraposisi dari proposisi berikut ini:</span>
<br />
<br />a) Jika hasil produksi melimpah maka harganya turun.
<br /> Invers : Jika hasil produksi tidak melimpah maka harganya naik.
<br /> Konvers : Jika harganya turun maka hasil produksi melimpah.
<br /> Kontraposisi : Jika harganya naik maka hasil produksi tidak melimpah.
<br />
<br />b) Jika lapangan pekerjaan tidak banyak maka pengangguran meningkat.
<br /> Invers : Jika lapangan pekerjaan banyak maka pengangguran menurun.
<br /> Konvers : Jika pengangguran meningkat maka lapangan pekerjaan sedikit.
<br /> Kontraposisi : Jika pengangguran menurun maka lapangan pekerjaan banyak.
<br />
<br />c) Jika ABCD bujur sangkar maka ABCD segi empat.
<br /> Invers : Jika ABCD bukan bujur sangkar maka ABCD bukan segi empat.
<br /> Konvers : Jika ABCD segi empat maka ABCD bujur sangkar.
<br /> Kontraposisi : Jika ABCD bukan segi empat maka ABCD bukan bujur sangkar.
<br />
<br /><meta equiv="CONTENT-TYPE" content="text/html; charset=utf-8"><title></title><meta name="GENERATOR" content="OpenOffice.org 2.2 (Linux)"><meta name="AUTHOR" content="user21"><meta name="CREATED" content="20090915;11345900"><meta name="CHANGED" content="16010101;0"><style type="text/css"> <!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --> </style> <meta equiv="CONTENT-TYPE" content="text/html; charset=utf-8"><title></title><meta name="GENERATOR" content="OpenOffice.org 2.2 (Linux)"><meta name="AUTHOR" content="user21"><meta name="CREATED" content="20090915;11345900"><meta name="CHANGED" content="16010101;0"><style type="text/css"> <!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --></style> d) Jika x>10 maka x²>100
<br /> Invers : Jika x≤10 maka x²≤100.
<br /> Konvers : Jika x²>100 maka x>10.
<br /> Kontraposisi : Jika x²≤100 maka x≤10.
<br />
<br />e) Jika x²-16=0 maka x=4 atau x=-4.
<br /> Invers : Jika x²-16≠0 maka x≠4 dan x≠-4.
<br /> Konvers : Jika x=4 atau x=-4 maka x²-16=0.
<br /> Kontraposisi : Jika x≠4 dan x≠-4 maka x²-16≠0.
<br />
<br /><meta equiv="CONTENT-TYPE" content="text/html; charset=utf-8"><title></title><meta name="GENERATOR" content="OpenOffice.org 2.2 (Linux)"><meta name="AUTHOR" content="user21"><meta name="CREATED" content="20090915;11345900"><meta name="CHANGED" content="16010101;0"><style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style> f) Jika sin x=90°-cos x maka x merupakan sudut lancip.
<br /><style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style> Invers : Jika sin x≠90°-cos x maka x bukan sudut lancip.
<br /><style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style> Konvers : Jika x merupakan sudut lancip maka sin x=90°-cos x.
<br /><style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style> Kontraposisi : Jika x bukan sudut lancip maka sin x≠90°-cos x.
<br />
<br />g) Jika tan x=-1 maka x=135<style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style><sup><span style="font-family:DejaVu Sans,sans-serif;"></span></sup>° dan x=315°.
<br /><style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style><style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style> Invers : Jika tan x≠-1 maka x≠135° atau x≠315°.
<br /> Konvers : Jika x=135<style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style>° dan x=315° maka tan x=-1.
<br /> Kontraposisi : Jika x≠135<style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style>° atau x≠315<style type="text/css"><!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } --</style>° maka tan x≠-1.
<br />the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com2tag:blogger.com,1999:blog-8107356043841146965.post-69865350582406694812009-09-08T11:31:00.004+07:002009-09-08T12:17:23.986+07:00TUGAS 1 PDM1) Kalimat Pernyataan<br /> - Umur bulan Januari adalah 30 hari<br /> - 3 adalah kelipatan 9<br /> - 6+7=13<br /> - Terdapat x bilangan real yang memenuhi 2x-1=5<br /> - 28 adalah faktor dari 4<br /><br />2) Kalimat Harapan<br /> - Semoga kita mendapat nilai ujian yang baik<br /> - Setelah lulus semoga sukses mendapat pekerjaan yang bagus<br /> - Jadilah kamu wisudawan terbaik<br /> - Selesaikan pendidikan dengan baik<br /> - Semoga kita lulus dalam 3,5 tahun<br /><br />3) Kalimat Terbuka<br /> - 4+x=7<br /> - p<5<br /> - x-5<7<br /> - 2x+10>6<br /> - 2x=7<br /><br />4) Kalimat Faktual<br /> - Manusia makan nasi<br /> - Binatang makan rumput<br /> - Kendaraan mengeluarkan asap<br /> - Tumbuhan melakukan fotosintesis<br /> - Minuman rasanya manis<br /><br />5) Kalimat Perintah<br /> - Tutup pintunya!<br /> - Kerjakan soal-soal di papan tulis sekarang!<br /> - Bersihkan meja dosen!<br /> - Berikan satu contoh kalimat terbuka!<br /> - Jelaskan proses pembuatan blog!<br /><br />6) Kalimat Tanya<br /> - Adakah penyelesaian dari x+7>20?<br /> - Berapa jumlah kakakmu?<br /> - Mengapa 2 termasuk bilangan prima?<br /> - Apakah 3 adalah faktor dari 15?<br /> - Siapa penemu lampu listrik?<br /><br /><br /><br /><br /><span style="font-style: italic; font-weight: bold;">NEGASI<br /></span>1. Bangun ABCD persegi panjang dan bangun ABC segitiga.<br /> <span style="font-style: italic;">Ingkaran: </span>Bangun ABCD bukan persegi panjang atau bangun ABC bukan segitiga<br />2. Jumlah sudut dalam segitiga adalah 180 atau ∠A+∠B+∠C=180<br /> <span style="font-style: italic;">Ingkaran: </span>Jumlah sudut dalam segitiga tidak 180 dan ∠A+∠B+∠C≠180<br />3. Besok ulangan PDM dan praktikum fisika.<br /> <span style="font-style: italic;">Ingkaran: </span>Besok tidak ulangan PDM atau tidak praktikum fisika.<br />4. Putri gemar matematika atau gemar fisika.<br /> <span style="font-style: italic;">Ingkaran: </span>Putri tidak gemar matematika dan tidak gemar fisika.<br /><br /><br /><br /><span style="font-weight: bold; font-style: italic;">DISJUNGSI EKSKLUSIF<br /></span>1. p: Ani pergi ke pesta teman<br /> q: Ani mengerjakan tugas<br /> p∨q: Ani pergi ke pesta teman atau mengerjakan tugas<br /><br />2. p: Ani kuliah di UNNES<br /> q: Ani kuliah di UI<br /> p∨q: Ani kuliah di UNNES atau di UI<br /><br /><br /><br /><br /><span style="font-weight: bold; font-style: italic;">DISJUNGSI INKLUSIF<br /></span>1. p: Gadis itu memakai jilbab putih<br /> q: Gadis itu memakai sepatu hitam<br /> p∨q: Gadis itu memakai jilbab putih atau memakai sepatu hitam<br /><br />2. p: Tyas makan sahur<br /> q: Tyas menonton televisi<br /> p∨q: Tyas makan sahur atau menonton televisi.<br /><span style="font-weight: bold; font-style: italic;"></span><span style="font-style: italic; font-weight: bold;"></span>the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com0tag:blogger.com,1999:blog-8107356043841146965.post-43299360136025727272009-09-01T12:21:00.000+07:002009-09-01T12:36:34.536+07:00Kelompok 61) Santi Noviyanti (4101409076)<br />2) Tety Dwi S. (4101409082)<br />3) Rizka Yuliana (4101409084)<br />4) Setiasih Alfindah (4101409096)<br />the fun Mathhttp://www.blogger.com/profile/03186948545871892325noreply@blogger.com0