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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers graphie-geometry math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Angle Bisector Theorem</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="ANGLES" data-ensure="ANGLES[ 0 ] % 2 === 0">randomTriangleAngles.triangle()</var>
<var id="SIDES_B">[ [ 0, 1 ], [] ]</var>
<var id="SIDES_C">[ [ 1 ], [ 2] ]</var>
<var id="TR_A">
function(){
var trA = new Triangle( [ 5, -8 ], ANGLES , 14 , {} );
trA.boxOut( [ [ [ 0, -10 ], [ 0, 10 ] ] ], [ 0.4 , 0 ] );
trA.boxOut( [ [ [ 11 , -10 ], [ 11, 10 ] ] ], [ -0.4 , 0 ] );
return trA;
}()
</var>
<var id="POINT_D">
function(){
var pointD = findIntersection( bisectAngle( TR_A.sides[ 0 ], reverseLine( TR_A.sides[ 2 ] ), 1 ), TR_A.sides[ 1 ] );
return pointD;
}()
</var>
<var id="TR_B">
function(){
var trB = new Triangle( [0,0],[], 3, {}, [ TR_A.points[ 0 ], TR_A.points[ 1 ], POINT_D ] );
trB.labels = { "angles" : clearArray( trB.niceAngles, [ 0 ] ), "sides" : mergeArray( clearArray( trB.niceSideLengths, SIDES_B[ 0 ] ), clearArray( [ "?", "?", "?" ], SIDES_B[ 1 ] ) ), "points": [ "A", "B", "D" ] };
return trB;
}()
</var>
<var id="TR_C">
function(){
var trC = new Triangle( [0,0],[], 3, {}, [ TR_A.points[ 0 ], POINT_D, TR_A.points[ 2 ] ] );
trC.labels = { "angles" : clearArray( trC.niceAngles, [ 0 ] ) , "sides" : mergeArray( clearArray( trC.niceSideLengths, SIDES_C[ 0 ] ), clearArray( [ "?", "?", "?" ], SIDES_C[ 1 ] ) ), "points": [ "", "", "C" ] };
return trC;
}()
</var>
<var id="TEMP_BD">TR_B.niceSideLengths[ 1 ]</var>
<var id="TEMP_AB">TR_B.niceSideLengths[ 0 ]</var>
<var id="TEMP_CD">TR_C.niceSideLengths[ 1 ]</var>
<var id="TEMP_AC">TR_C.niceSideLengths[ 2 ]</var>
<var id="BD">TR_B.niceSideLengths[ 1 ]</var>
<var id="AB">TR_B.niceSideLengths[ 0 ]</var>
<var id="CD">TR_C.niceSideLengths[ 1 ]</var>
<var id="AC">TR_C.niceSideLengths[ 2 ]</var>
</div>
<div class="problem">
What is the length of the side AC?
</div>
<div class="question">
<div class="graphie">
init({
range: TR_A.boundingRange(1.5)
})
TR_B.draw();
TR_B.drawLabels();
TR_C.draw();
TR_C.drawLabels();
</div>
</div>
<div class="hints">
<p>Angles <code>DAB</code> and <code>DAC</code> are equal.</p>
<p>Therefore <code>AD</code> is the bisector of <code>CAB</code></p>
<p>Angle Bisector Theorem states that <code>\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }</code></p>
</div>
<div class="problems">
<div id="AC">
<div class="vars">
<var id="AC">roundTo( 1, TEMP_AB * TEMP_CD / TEMP_BD )</var>
</div>
<div class="problem">
What is the length of the side AC? (Round to 1 decimal place).
</div>
<div class="solution"><var>AC</var></div>
<div class="hints" data-apply="appendContents">
<p><code>\dfrac{ <var>AB</var> }{ <var>BD</var> } = \dfrac{ AC }{ <var>CD</var> }</code></p>
<p><code>AC = \dfrac{<var>AB</var> \cdot <var>CD</var> }{ <var>BD</var> }</code></p>
<p><code>AC = <var>AC </var></code></p>
</div>
</div>
<div id="AB">
<div class="vars">
<var id="AB">roundTo( 1, TEMP_AC * TEMP_BD / TEMP_CD )</var>
<var id="SIDES_B">[ [ 1 ], [0] ]</var>
<var id="SIDES_C">[ [ 1,2 ], [ ] ]</var>
</div>
<div class="problem">
What is the length of the side AB? (Round to 1 decimal place).
</div>
<div class="solution"><var>AB</var></div>
<div class="hints" data-apply="appendContents">
<p><code>\dfrac{ AB }{ <var>BD</var> } = \dfrac{ <var>AC</var> }{ <var>CD</var> }</code></p>
<p><code>AB = \dfrac{ <var>AC</var> \cdot <var>BD</var> }{ <var>CD</var> }</code></p>
<p><code>AB = <var>AB </var></code></p>
</div>
</div>
<div id="CD">
<div class="vars">
<var id="CD">roundTo( 1, TEMP_AC * TEMP_BD / TEMP_AB )</var>
<var id="SIDES_B">[ [ 1, 0 ], [] ]</var>
<var id="SIDES_C">[ [ 2 ], [1 ] ]</var>
</div>
<div class="problem">
What is the length of the side CD? (Round to 1 decimal place).
</div>
<div class="solution"><var>CD</var></div>
<div class="hints" data-apply="appendContents">
<p><code>\dfrac{ <var> AB</var> }{ <var>BD</var> } = \dfrac{ <var>AC</var> }{ CD }</code></p>
<p><code>CD = \dfrac{ <var>AC</var> \cdot <var>BD</var> }{ <var>AB</var> }</code></p>
<p><code>CD = <var>CD </var></code></p>
</div>
</div>
<div id="BD">
<div class="vars">
<var id="BD">roundTo( 1, TEMP_AB * TEMP_CD / TEMP_AC )</var>
<var id="SIDES_B">[ [ 0 ], [ 1 ] ]</var>
<var id="SIDES_C">[ [ 1, 2 ], [ ] ]</var>
</div>
<div class="problem">
What is the length of the side BD? (Round to 1 decimal place).
</div>
<div class="solution"><var>BD</var></div>
<div class="hints" data-apply="appendContents">
<p><code>\dfrac{ <var> AB</var> }{ BD } = \dfrac{ <var>AC</var> }{ <var>CD</var> }</code></p>
<p><code>BD = \dfrac{ <var>AB</var> \cdot <var>CD</var> }{ <var>AC</var> }</code></p>
<p><code>BD = <var>BD</var></code></p>
</div>
</div>
</div>
</div>
</body>
</html>
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