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<title>Perpendicular and Parallel</title>
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<h1 align="center">Perpendicular and Parallel</h1>
<h2>Perpendicular</h2>
<p>It just means <b>at right angles (90&deg;) to</b>.</p>
<p>The red line is perpendicular to the blue line:</p>
<p class="center"><img src="geometry/images/perpendicular.svg" alt="Perpendicular Examples" /></p>
<p>Here also:
</p>
<p class="center"><img src="geometry/images/perpendicular-also.svg" alt="Perpendicular Examples" /></p>
<p>(The little box drawn in the corner, means &quot;at right angles&quot;,
so we didn't really need to <i>also</i> show that it was 90&deg;,
but we just wanted to!)</p>
<p>Try for yourself:</p>
<iframe src="geometry/igeom-perp.html" scrolling="no" style="width:362px; height:302px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
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<h2>Parallel</h2>
<p>Lines are parallel if they are always the same distance apart (called &quot;equidistant&quot;), and will never meet. (They also point in the same direction). Just remember:</p>
<h3 align="center">Always the same distance apart and never touching<i>.</i></h3>
<p>The red line and blue line are parallel in both these examples:</p>
<div class="simple">
<table border="0" align="center">
<tr align="center">
<td><img src="geometry/images/parallel.svg" alt="Parallel Example 1" /></td>
<td width="50" bgcolor="#FFFFFF"><font color="#FFFFFF"></font></td>
<td><img src="geometry/images/parallel-also.svg" alt="Parallel Example 2" /></td>
</tr>
<tr align="center">
<td>
<div align="center">Example 1</div>
</td>
<td width="30" bgcolor="#FFFFFF">
<div align="center"><font color="#FFFFFF"></font></div>
</td>
<td>
<div align="center">Example 2</div>
</td>
</tr>
</table>
</div>
<p>Try it yourself:</p>
<iframe src="geometry/igeom-parallel.html" scrolling="no" style="width:362px; height:302px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
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--><h2>Perpendicular to Parallel</h2>
<p><i>Question:</i> What is the difference between perpendicular and
parallel? <b><br />
</b><i>Answer:</i><b> 90 degrees</b> (a <i>right angle</i>)</p>
<p>That's right, when we rotate a perpendicular line by 90&deg; it
becomes parallel (but not if it touches!)</p>
<table border="0" align="center" cellpadding="10">
<tr>
<td height="135"><img src="images/parallel-rotate-1.gif" width="130" height="95" alt="Perpendicular" /></td>
<td height="135"><img src="images/parallel-rotate-2.gif" width="167" height="100" alt="Rotate 90 Degrees" /></td>
<td height="135"><br />
<br />
<img src="images/parallel-rotate-3.gif" width="166" height="36" alt="Parallel" /></td>
</tr>
<tr>
<td height="32">
<div align="center"><b>Perpendicular ...</b></div>
</td>
<td height="32">
<div align="center"><b>Rotate One Line 90&deg;</b></div>
</td>
<td height="32">
<div align="center"><b>... Parallel !</b></div>
</td>
</tr>
</table>
<p>Likewise, parallel lines become perpendicular when one line is rotated 90&deg;.</p>
<h2>Parallel Curves</h2>
<p>Curves can also be parallel when they keep the same distance
apart (called &quot;equidistant&quot;), like
railroad tracks.</p>
<p>The red curve is parallel to the blue curve in both these cases:</p>
<table border="0" cellpadding="20" align="center">
<tr>
<td height="95"><img src="geometry/images/parallel-curves.svg" alt="Parallel Curves Example 1" /></td>
<td height="95"><img src="geometry/images/concentric-circles.svg" alt="Parallel Curves Example 1" /></td>
</tr>
</table>
<h2>Parallel Surfaces</h2>
<p>Surfaces can also be parallel, like this:<i></i></p>
<p class="center"><img src="images/parallel-surfaces.gif" width="211" height="164" alt="Parallel Surfaces" /></p>
<p style="float:left; margin: 0 10px 5px 0;"><img src="geometry/images/plane-perp-4.gif" width="275" height="201" alt="plane perpendicular" /></p>
<h2>Lines and Planes</h2>
Advanced Topic: You can also learn about <a href="geometry/parallel-perpendicular-lines-planes.html">Parallel and Perpendicular Lines and Planes</a>
<div style="clear:both"></div>
<p>&nbsp;</p>
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<script type="text/javascript">getQ(9519, 9520, 9521, 9522, 9523, 9524, 9525, 9526);</script>&nbsp;
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<div class="related">
<a href="geometry/parallel-lines.html">Parallel Lines and Pairs of Angles</a>
<a href="geometry/parallel-perpendicular-lines-planes.html">Parallel and Perpendicular Lines and Planes</a>
<a href="algebra/line-parallel-perpendicular.html">Finding Parallel and Perpendicular Lines Using Algebra</a>
<a href="geometry/index.html">Geometry Index</a>
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