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<title>Parallel Lines, and Pairs of Angles</title>
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<h1 align="center">Parallel Lines, and Pairs of Angles</h1>
<h2>Parallel Lines</h2>
<p><a href="line.html">Lines</a> are parallel if they are always the same distance apart (called &quot;equidistant&quot;), and will never meet. Just remember: </p>
<h3 align="center">Always the same distance apart and never touching<i>.</i></h3>
<p>The red line is parallel to the blue line in each of these examples:</p>
<div class="simple">
<table border="0" align="center">
<tr align="center">
<td><img src="images/parallel.svg" alt="Parallel Example 1" /></td>
<td width="30"><font color="#FFFFFF"></font></td>
<td><img src="images/parallel-also.svg" alt="Parallel Example 2" /></td>
</tr>
<tr align="center">
<td><div align="center">Example 1</div></td>
<td width="30"><div align="center"><font color="#FFFFFF"></font></div></td>
<td><div align="center">Example 2</div></td>
</tr>
</table>
</div>
<p>Parallel lines also point in the same direction.</p>
<div class="fun">
Parallel lines have so much in common. It's a shame they will never meet!</div>
<h3>Try it yourself:</h3>
<iframe src="igeom-parallel.html" scrolling="no" style="width:362px; height:302px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
<h2>Pairs of Angles</h2><p style="float:right; margin: 0 0 5px 10px;"><img src="images/parallel-angle-example.svg" alt="parallel lines angle example" /></p>
<p>When parallel lines get crossed by another line (which is called a <a href="transversal.html">Transversal</a>), you can see that many angles are the same, as in this example:</p>
<p>&nbsp;</p>
<p>These angles can be made into <b>pairs of angles</b> which have special names. </p>
<div style="clear:both"></div>
<p>Click on each name to see it highlighted:</p>
<iframe src="iparallel-pair.html" scrolling="no" style="width:422px; height:302px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
<p>Now play with it here. Try dragging the points, and choosing different angle types. You can also turn "Parallel" off or on:</p>
<script>geomlineparaMain('all');</script>
<h2>Testing for Parallel Lines</h2>
Some of those special <b>pairs of angles</b> can be used to test if lines really are parallel: <br />
<br />
<div class="simple">
<table border="0" align="center">
<tr>
<td valign="top"><table border="0">
<tr align="center">
<td class="larger">If <b>Any Pair</b> Of ...</td>
<td><i>Example:</i></td>
</tr>
<tr align="center">
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td><a href="corresponding-angles.html">Corresponding Angles</a> are equal</td>
<td><i>a = e</i></td>
</tr>
<tr align="center">
<td>or</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td><a href="alternate-interior-angles.html">Alternate Interior Angles</a> are equal</td>
<td><i>c = f</i></td>
</tr>
<tr align="center">
<td>or</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td><a href="alternate-exterior-angles.html">Alternate Exterior Angles</a> are equal</td>
<td><i>b = g</i></td>
</tr>
<tr align="center">
<td>or</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td><a href="consecutive-interior-angles.html">Consecutive Interior Angles</a> add up to 180&deg;</td>
<td><i>d + f = 180&deg;</i></td>
</tr>
<tr align="center">
<td class="larger">&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td colspan="2" class="larger">... then the lines are <b>Parallel</b><i></i></td>
</tr>
</table></td>
<td valign="middle"><img src="images/parallel-lines-pair.svg" alt="parallel angle pairs" /></td>
</tr>
</table>
</div>
<h2>Examples</h2>
<div class="beach">
<table border="0" align="center">
<tr>
<td width="220" align="right">These lines <b>are</b> parallel, because a pair of <a href="corresponding-angles.html">Corresponding Angles</a> are equal.</td>
<td width="220"><img src="images/parallel-angle-example3.gif" width="219" height="200" alt="parallel angle example 110 110" /></td>
</tr>
<tr>
<td width="220" align="right"><img src="images/parallel-angle-example2.gif" width="200" height="199" alt="not parallel angle 81 101" /></td>
<td width="220">These lines are <b>not</b> parallel, because a pair of <a href="consecutive-interior-angles.html">Consecutive Interior Angles</a> do not add up to 180&deg; (81&deg; + 101&deg; =182&deg;)</td>
</tr>
<tr>
<td width="220" align="right">These lines <b>are</b> parallel, because a pair of <a href="alternate-interior-angles.html">Alternate Interior Angles</a> are equal</td>
<td width="220"><img src="images/parallel-angle-example1.gif" width="220" height="200" alt="parallel angle example 70 70" /></td>
</tr>
</table>
</div>
<p>&nbsp;</p>
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<script type="text/javascript">getQ(813, 814, 1783, 3298, 815, 816, 1784, 1785, 3299, 3300);</script>&nbsp; </div>
<div class="related"> <a href="../angle180.html">Angles On a Straight Line</a> <a href="../angle360.html">Angles Around a Point</a> <a href="transversal.html">Transversal</a> <a href="congruent-angles.html">Congruent Angles</a> <a href="vertical-angles.html">Vertical Angles</a> <a href="index.html">Geometry Index</a> </div>
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