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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>Congruent triangles 1</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="MAIN">randomTriangleAngles.triangle()</var>
<var id="MAIN_SIZE">6 + random() * 2</var>
<var id="IS_B">randRange( 0, 1 ) === 1</var>
<var id="B">IS_B ? MAIN : randomTriangleAngles.triangle()</var>
<var id="B_SIZE">IS_B ? MAIN_SIZE : 6 + random() * 2</var>
<var id="CHOICES">[i18n._("Yes"), i18n._("No"), i18n._("There is not enough information to say")]</var>
<var id="ANSWER">IS_B ? 0 : 1</var>
<var id="A_ANGLES">[ 0, 1, 2 ]</var>
<var id="B_ANGLES">A_ANGLES</var>
<var id="A_SIDES">[ 0, 1, 2 ]</var>
<var id="B_SIDES">A_SIDES</var>
<var id="TR_A">
function(){
var t = new Triangle( [ 3, -2 ], MAIN, MAIN_SIZE, {} );
t.labels = { "name": "A", "angles" : clearArray( t.niceAngles, A_ANGLES ), "sides" : clearArray( t.niceSideLengths, A_SIDES ) };
return t;
}()
</var>
<var id="TR_B">
function(){
var t = new Triangle( [ 7, -7 ], B, B_SIZE, {} );
t.labels = { "name": "B", "angles" : clearArray( t.niceAngles, B_ANGLES ), "sides" : clearArray( t.niceSideLengths, B_SIDES ) };
return t;
}()
</var>
</div>
<div class="hints">
<p>Triangles are congruent when all corresponding sides and interior angles are congruent. </p>
<p>However, we do not need to know all the values in order to determine whether two triangles are congruent. </p>
<p>The rules we use for determining congruency are SSS, ASA, SAS and AAS</p>
</div>
<p class="question">
Are these two triangles congruent?
</p>
<p class="render-answer-area-here"></p>
<div class="problem">
<div class="graphie">
TR_A.rotate( randRange( 0, 360 ) );
TR_B.rotate( randRange( 0, 360 ) );
var aBounding = TR_A.boundingRange(1);
var bBounding = TR_B.boundingRange(1);
var minX = Math.min(aBounding[0][0], bBounding[0][0]);
var maxX = Math.max(aBounding[0][1], bBounding[0][1]);
var minY = Math.min(aBounding[1][0], bBounding[1][0]);
var maxY = Math.max(aBounding[1][1], bBounding[1][1]);
init({
range: [ [minX, maxX ], [ minY, maxY ] ]
})
TR_A.draw();
TR_A.drawLabels();
TR_B.draw();
TR_B.drawLabels();
</div>
</div>
<div class="solution"><var>CHOICES[ANSWER]</var></div>
<ul class="choices" data-category="true">
<li data-each="CHOICES as choice">
<var>choice</var>
</li>
</ul>
<div class="problems">
<div id="SSS">
<div class="vars">
<var id="A_ANGLES">[]</var>
<var id="A_SIDES">[ 0, 1, 2 ]</var>
</div>
<div class="hints" data-apply="appendContents">
<p>In this problem we are given the sides of the triangles, so we can compare them easily.</p>
<p data-if="IS_B">Triangle B has 3 sides the same as triangle A, so they are congruent.</p>
<p data-else="">Because the sides do not match, triangle B is not congruent with triangle A.</p>
</div>
</div>
<div id="SAS">
<div class="vars">
<var id="A_ANGLES">[ 1 ]</var>
<var id="A_SIDES">[ 0, 1 ]</var>
</div>
<div class="hints" data-apply="appendContents">
<p>In this problem we are given two sides and an angle between them, so we can use the SAS rule.</p>
<p data-if="IS_B">Triangle B has those two sides and the angle the same as triangle A, so they are congruent.</p>
<p data-else="">Because the sides and the angle do not match, triangle A is not congruent with triangle B.</p>
</div>
</div>
<div id="ASA">
<div class="vars">
<var id="A_ANGLES">[ 0, 1 ]</var>
<var id="A_SIDES">[ 0 ]</var>
</div>
<div class="hints" data-apply="appendContents">
<p>In this problem we are given two angles and as side between them, so we can use the ASA rule.</p>
<p data-if="IS_B">Triangle B has those two angles and the side the same as triangle A, so they are congruent.</p>
<p data-else="">Because the angles and the side do not match, triangle A is not congruent with triangle B.</p>
</div>
</div>
<div id="AAS">
<div class="vars">
<var id="A_ANGLES">[ 0, 1 ]</var>
<var id="A_SIDES">randRange( 0, 1 ) === 1 ? [ 2 ] : [ 1 ]</var>
</div>
<div class="hints" data-apply="appendContents">
<p>In this problem we are given two angles and another side so we can use the AAS rule.</p>
<p data-if="IS_B">Triangle B has those two angles and the side the same as triangle A, so they are congruent.</p>
<p data-else="">Because the angles and the side do not match, triangle A is not congruent with triangle B.</p>
</div>
</div>
<div id="AAA">
<div class="vars">
<var id="A_ANGLES">[ 0, 1, 2 ]</var>
<var id="A_SIDES">[ ]</var>
<var id="ANSWER">IS_B ? 2 : 1</var>
</div>
<div class="hints" data-apply="appendContents">
<p>In this problem we know all three triangle angles.</p>
<div data-if="IS_B" data-unwrap="">
<p>
However, having all three angles the same is not a property we can use to conclude that two triangles are congruent. We can only say for sure that they are similar.
</p>
<p>We do not have enough information to say that the two triangles are congruent.</p>
</div>
<p data-else="">Because the angles do not match, triangle A is not congruent with triangle B.</p>
</div>
</div>
</div>
</div>
</body>
</html>