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<!DOCTYPE html>
<html data-require="math graphie expressions">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Congruent segments</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
<style>
.lcol { text-align:left; width:200px; display:inline-block; }
.rcol { text-align:left; width:auto; display:inline-block; }
</style>
</head>
<body>
<div class="exercise">
<div class="problems">
<div>
<div class="vars">
<var id="YES,NO">[$._("Yes"), $._("No")]</var>
<var id="SOLUTION">random() &lt; 0.5 ? YES : NO</var>
<div data-ensure="( SOLUTION === YES &amp;&amp; POINTS[ 1 ] - POINTS[ 0 ] === POINTS[ 3 ] - POINTS[ 2 ] ) || ( SOLUTION === NO &amp;&amp; POINTS[ 1 ] - POINTS[ 0 ] !== POINTS[ 3 ] - POINTS[ 2 ] )">
<var id="POINTS">sortNumbers( randRangeUnique( -5, 5, 4 ) )</var>
</div>
<var id="COLORS">[ BLUE, GREEN, PINK, ORANGE ]</var>
</div>
<p class="question">Are <code>\overline{AB}</code> and <code>\overline{CD}</code> congruent?</p>
<p class="render-answer-area-here"></p>
<div class="problem">
<div class="graphie" id="number-line">
init({
range: [ [ -6, 6 ], [ -1, 1 ] ]
});
style({ stroke: "#999" });
line( [ -5, 0 ], [ 5, 0 ] );
for ( var x = -5; x &lt;= 5; x++ ) {
line( [ x, -0.2 ], [ x, 0.2 ] );
label( [ x, -0.53 ], String( x ).replace( /-(\d)/g, "\\llap{-}$1" ), "center", { color: "#999" } );
}
style({ strokeWidth: 3.5 });
line( [ 0, -0.2], [0, 0.2]);
style({ stroke: COLORS[ 0 ], fill: COLORS[ 0 ] });
circle( [ POINTS[ 0 ], 0 ], 0.10 );
style({ stroke: COLORS[ 1 ], fill: COLORS[ 1 ] });
circle( [ POINTS[ 1 ], 0 ], 0.10 );
style({ stroke: COLORS[ 2 ], fill: COLORS[ 2 ] });
circle( [ POINTS[ 2 ], 0 ], 0.10 );
style({ stroke: COLORS[ 3 ], fill: COLORS[ 3 ] });
circle( [ POINTS[ 3 ], 0 ], 0.10 );
label( [ POINTS[ 0 ], 0 ], "A", "above", { color: COLORS[ 0 ] } );
label( [ POINTS[ 1 ], 0 ], "B", "above", { color: COLORS[ 1 ] } );
label( [ POINTS[ 2 ], 0 ], "C", "above", { color: COLORS[ 2 ] } );
label( [ POINTS[ 3 ], 0 ], "D", "above", { color: COLORS[ 3 ] } );
</div>
</div>
<div class="solution"><var>SOLUTION</var></div>
<ul class="choices" data-category="true">
<li><var>YES</var></li>
<li><var>NO</var></li>
</ul>
<div class="hints">
<p>Congruent segments have equal lengths.</p>
<div>
<p>Find the lengths of <code>\overline{AB}</code> and <code>\overline{CD}</code>:</p>
<p>
<span class="lcol"><code>AB = |\color{<var>COLORS[ 0 ]</var>}{<var>POINTS[ 0 ]</var>} - \color{<var>COLORS[ 1 ]</var>}{<var>POINTS[ 1 ]</var>}|</code></span>
<span class="rcol"><code>CD = |\color{<var>COLORS[ 2 ]</var>}{<var>POINTS[ 2 ]</var>} - \color{<var>COLORS[ 3 ]</var>}{<var>POINTS[ 3 ]</var>}|</code></span>
</p>
</div>
<p>
<span class="lcol"><code>AB = |<var>POINTS[ 0 ] - POINTS[ 1 ]</var>|</code></span>
<span class="rcol"><code>CD = |<var>POINTS[ 2 ] - POINTS[ 3 ]</var>|</code></span>
</p>
<p>
<span class="lcol"><code>AB = <var>POINTS[ 1 ] - POINTS[ 0 ]</var></code></span>
<span class="rcol"><code>CD = <var>POINTS[ 3 ] - POINTS[ 2 ]</var></code></span>
</p>
<div data-if="SOLUTION === YES" data-unwrap="">
<p><code>AB = CD</code></p>
<p class="final_answer">Yes, <code>\overline{AB}</code> and <code>\overline{CD}</code> are congruent.</p>
</div>
<div data-else="" data-unwrap="">
<p><code>AB \neq CD</code></p>
<p class="final_answer">No, <code>\overline{AB}</code> and <code>\overline{CD}</code> are not congruent.</p>
</div>
</div>
</div>
</div>
</div>
</body>
</html>
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