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parallel_lines_1.html
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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers angles">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Parallel lines 1</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="corresponding-angles">
<div class="vars">
<var id="ANCHOR">randRange( 20, 160 )</var>
<var id="KNOWN_INDEX">randRange( 0, 7 )</var>
<var id="UNKNOWN_INDEX">( KNOWN_INDEX + 4 ) % 8</var>
<var id="MEASURE">KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR</var>
</div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question" data-if="KNOWN_INDEX < 4">If we know that the <span class="hint_blue">bottom marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the top marked angle</span>?</p>
<p class="question" data-else="">If we know that the <span class="hint_blue">top marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the bottom marked angle</span>?</p>
<p class="solution" data-forms="integer"><var>MEASURE</var></p>
<div class="graphie" id="parallel-lines">
init({
range: [ [ -1, 11 ], [-1, 4] ]
});
graph.pl = new ParallelLines( 0, 0, 10, 0, 3 );
graph.pl.draw();
graph.pl.drawMarkers(ANCHOR);
graph.pl.drawTransverse( ANCHOR );
graph.pl.drawAngle( KNOWN_INDEX, true );
graph.pl.drawAngle( UNKNOWN_INDEX, false, RED );
</div>
<div class="hints">
<p>Notice that the two angles are in the same position but at different intersections.</p>
<p>One way to describe the angles is to say that they are corresponding angles.</p>
<p>Corresponding angles are always equal.</p>
<div>
<p data-if="KNOWN_INDEX < 4">The top angle measures <code><var>MEASURE</var></code> degrees.</p>
<p data-else="">The bottom angle measures <code><var>MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAngle( UNKNOWN_INDEX, true, RED );
</div>
</div>
</div>
</div>
<div id="alternate-interior-angles">
<div class="vars">
<var id="ANCHOR">randRange( 20, 160 )</var>
<var id="KNOWN_INDEX, UNKNOWN_INDEX">shuffle( randFromArray( [ [ 2, 4 ], [ 3, 5 ] ] ) )</var>
<var id="MEASURE">KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR</var>
</div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question" data-if="KNOWN_INDEX < 4">If we know that the <span class="hint_blue">bottom marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the top marked angle</span>?</p>
<p class="question" data-else="">If we know that the <span class="hint_blue">top marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the bottom marked angle</span>?</p>
<p class="solution" data-forms="integer"><var>MEASURE</var></p>
<div class="graphie" id="parallel-lines">
init({
range: [ [ -1, 11 ], [-1, 4] ]
});
graph.pl = new ParallelLines( 0, 0, 10, 0, 3 );
graph.pl.draw();
graph.pl.drawMarkers(ANCHOR);
graph.pl.drawTransverse( ANCHOR );
graph.pl.drawAngle( KNOWN_INDEX, true );
graph.pl.drawAngle( UNKNOWN_INDEX, false, RED );
</div>
<div class="hints">
<div>
<p>Vertical angles are equal, so the pink angle measures <code><var>MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawVerticalAngle( KNOWN_INDEX, true, PINK );
</div>
</div>
<p>The pink and red angles are corresponding angles, so they are also equal.</p>
<div>
<p data-if="KNOWN_INDEX < 4">The top angle measures <code><var>MEASURE</var></code> degrees.</p>
<p data-else="">The bottom angle measures <code><var>MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAngle( UNKNOWN_INDEX, true, RED );
</div>
</div>
</div>
</div>
<div id="alternate-exterior-angles">
<div class="vars">
<var id="ANCHOR">randRange( 20, 160 )</var>
<var id="KNOWN_INDEX, UNKNOWN_INDEX">shuffle( randFromArray( [ [ 2, 4 ], [ 3, 5 ] ] ) )</var>
<var id="MEASURE">KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR</var>
</div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question" data-if="KNOWN_INDEX < 4">If we know that the <span class="hint_blue">bottom marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the top marked angle</span>?</p>
<p class="question" data-else="">If we know that the <span class="hint_blue">top marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the bottom marked angle</span>?</p>
<p class="solution" data-forms="integer"><var>MEASURE</var></p>
<div class="graphie" id="parallel-lines">
init({
range: [ [ -1, 11 ], [-1, 4] ]
});
graph.pl = new ParallelLines( 0, 0, 10, 0, 3 );
graph.pl.draw();
graph.pl.drawMarkers(ANCHOR);
graph.pl.drawTransverse( ANCHOR );
graph.pl.drawAngle( KNOWN_INDEX, true );
graph.pl.drawAngle( UNKNOWN_INDEX, false, RED );
</div>
<div class="hints">
<div>
<p>Vertical angles are equal, so the pink angle measures <code><var>MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawVerticalAngle( KNOWN_INDEX, true, PINK );
</div>
</div>
<p>The pink and red angles are corresponding angles, so they are also equal.</p>
<div>
<p data-if="KNOWN_INDEX < 4">The top angle measures <code><var>MEASURE</var></code> degrees.</p>
<p data-else="">The bottom angle measures <code><var>MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAngle( UNKNOWN_INDEX, true, RED );
</div>
</div>
</div>
</div>
<div id="same-side-interior-angles">
<div class="vars">
<var id="ANCHOR">randRange( 20, 160 )</var>
<var id="KNOWN_INDEX, UNKNOWN_INDEX">shuffle( randFromArray( [ [ 1, 6 ], [ 0, 7 ] ] ) )</var>
<var id="MEASURE">KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR</var>
</div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question" data-if="KNOWN_INDEX < 4">If we know that the <span class="hint_blue">bottom marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the top marked angle</span>?</p>
<p class="question" data-else="">If we know that the <span class="hint_blue">top marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the bottom marked angle</span>?</p>
<p class="solution" data-forms="integer"><var>180 - MEASURE</var></p>
<div class="graphie" id="parallel-lines">
init({
range: [ [ -1, 11 ], [-1, 4] ]
});
graph.pl = new ParallelLines( 0, 0, 10, 0, 3 );
graph.pl.draw();
graph.pl.drawMarkers(ANCHOR);
graph.pl.drawTransverse( ANCHOR );
graph.pl.drawAngle( KNOWN_INDEX, true );
graph.pl.drawAngle( UNKNOWN_INDEX, false, RED );
</div>
<div class="hints">
<div>
<p>The pink angles are adjacent to the blue angle and form a straight line, so we know that they measure <code><var>180 - MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAdjacentAngles( KNOWN_INDEX, true, PINK );
</div>
</div>
<p>It makes sense that the pink angles are equal because they are opposite each other.</p>
<p>One of the pink angles corresponds with the red angle, and the other pink angle forms an alternate interior angle.</p>
<div>
<p data-if="KNOWN_INDEX < 4">The top angle equals the pink angles and measures <code><var>180 - MEASURE</var></code> degrees.</p>
<p data-else="">The top angle equals the pink angles and measures <code><var>180 - MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAngle( UNKNOWN_INDEX, true, RED );
</div>
<p>Note that the blue and red angles are supplementary.</p>
</div>
</div>
</div>
<div id="same-side-exterior-angles">
<div class="vars">
<var id="ANCHOR">randRange( 20, 160 )</var>
<var id="KNOWN_INDEX, UNKNOWN_INDEX">shuffle( randFromArray( [ [ 3, 4 ], [ 2, 5 ] ] ) )</var>
<var id="MEASURE">KNOWN_INDEX % 2 === 0 ? ANCHOR : 180 - ANCHOR</var>
</div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question" data-if="KNOWN_INDEX < 4">If we know that the <span class="hint_blue">bottom marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the top marked angle</span>?</p>
<p class="question" data-else="">If we know that the <span class="hint_blue">top marked angle is <code><var>MEASURE</var></code> degrees</span>, what is the <span class="hint_red">measure of the bottom marked angle</span>?</p>
<p class="solution" data-forms="integer"><var>180 - MEASURE</var></p>
<div class="graphie" id="parallel-lines">
init({
range: [ [ -1, 11 ], [-1, 4] ]
});
graph.pl = new ParallelLines( 0, 0, 10, 0, 3 );
graph.pl.draw();
graph.pl.drawMarkers(ANCHOR);
graph.pl.drawTransverse( ANCHOR );
graph.pl.drawAngle( KNOWN_INDEX, true );
graph.pl.drawAngle( UNKNOWN_INDEX, false, RED );
</div>
<div class="hints">
<div>
<p>The pink angles are adjacent to the blue angle and form a straight line, so we know that they measure <code><var>180 - MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAdjacentAngles( KNOWN_INDEX, true, PINK );
</div>
</div>
<p>It makes sense that the pink angles are equal because they are vertical angles.</p>
<p>One of the pink angles corresponds with the red angle, and the other pink angle forms an alternate exterior angle.</p>
<div>
<p>The bottom angle equals the pink angles and measures <code><var>180 - MEASURE</var></code> degrees.</p>
<div class="graphie" data-update="parallel-lines">
graph.pl.drawAngle( UNKNOWN_INDEX, true, RED );
</div>
<p>Note that the blue and red angles are supplementary.</p>
</div>
</div>
</div>
</div>
</div>
</body>
</html>