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217 lines
8.3 KiB
HTML
217 lines
8.3 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/geometry/symmetry-reflection.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:39:18 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<title>Reflection Symmetry</title>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Reflection Symmetry</h1>
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<h2>Reflection Symmetry</h2>
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<p><b>Reflection Symmetry</b> (sometimes called <i>Line Symmetry</i> or <i>Mirror Symmetry</i>) is easy to see, because one half is the reflection of the other half.</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><img src="images/flame-mirror.jpg" alt="dog mirror" height="214" width="156"></td>
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<td valign="top"> </td>
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<td valign="top">
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<p class="center"> </p>
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<p class="center">Here my dog "Flame" has her face made perfectly<br>
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symmetrical with a bit of photo magic.</p>
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<p class="center">The white line down the center is the <b>Line of Symmetry<br>
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</b> (also called the "Mirror Line")</p>
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</td>
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</tr>
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</tbody></table>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/reflection-parinacota.jpg" alt="reflection parinacota" height="205" width="299"></p>
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<p>The reflection in this lake also has symmetry, but in this case:</p>
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<ul>
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<li>the <b>Line of Symmetry</b> runs left-to-right</li>
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<li>it is not perfect symmetry, because the image is changed a little by the lake surface.</li>
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</ul>
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<h2>Line of Symmetry</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/xy-graph-line15.svg" alt="graph line of symmetry at an angle" height="152" width="152"></p>
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<span style="float:left; margin: 0 10px 5px 0;"></span>
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<p>The Line of Symmetry (also called the <b>Mirror Line</b>) can be in <b>any direction</b>.<br>
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<br>
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But there are four common directions, and they are named for the line they make on the standard XY graph.</p>
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<p>See these examples (the artwork was made using <a href="symmetry-artist.html">Symmetry Artist</a>) :</p>
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<div style="clear:both"></div>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>
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<div class="center"><b>Line of Symmetry</b></div>
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</td>
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<td>
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<div class="center"><b>Sample Artwork</b></div>
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</td>
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<td>
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<div class="center"><b>Example Shape</b></div>
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</td>
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</tr>
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<tr>
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<td><img src="images/xy-graph-x-axis.svg" alt="graph x axis" height="152" width="152"></td>
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<td><img src="images/symmetry-art-x.gif" alt="symmetry art x" height="151" width="151"></td>
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<td><img src="images/symmetry-shape-x.gif" alt="symmetry shape x" height="151" width="151"></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td><img src="images/xy-graph-y-axis.svg" alt="graph y axis" height="152" width="152"></td>
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<td><img src="images/symmetry-art-y.gif" alt="symmetry art y" height="151" width="151"></td>
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<td><img src="images/symmetry-shape-y.gif" alt="symmetry shape y" height="151" width="151"></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td><img src="images/xy-graph-x-y.svg" alt="graph y=x" height="152" width="152"></td>
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<td><img src="images/symmetry-art-yx.gif" alt="symmetry art y=x" height="151" width="151"></td>
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<td><img src="images/symmetry-shape-yx.gif" alt="symmetry shape y=x" height="151" width="151"></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td><img src="images/xy-graph-x-my.svg" alt="graph y=-x" height="152" width="152"></td>
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<td><img src="images/symmetry-art-ymx.gif" alt="symmetry art y=-x" height="151" width="151"></td>
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<td><img src="images/symmetry-shape-ymx.gif" alt="symmetry shape y=-x" height="151" width="151"></td>
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</tr>
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</tbody></table></div>
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<h2>Plane Shapes</h2>
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<p>Not all shapes have lines of symmetry, or they may have several lines of symmetry. For example, a <a href="../triangle.html">Triangle</a> can have <b>3</b>, or <b>1</b> or <b>no</b> lines of symmetry:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td><img src="images/symmetry-equilateral-triangle.gif" alt="symmetry equilateral triangle" height="130" width="130"></td>
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<td> </td>
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<td><img src="images/symmetry-isosceles-triangle.gif" alt="symmetry isosceles triangle" height="130" width="131"></td>
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<td> </td>
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<td><img src="images/symmetry-scalene-triangle.gif" alt="no symmetry scalene triangle" height="130" width="130"></td>
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</tr>
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<tr style="text-align:center;">
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<td><b>Equilateral Triangle</b><br>
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(all sides equal,<br>
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all angles equal) </td>
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<td> </td>
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<td><b>Isosceles Triangle</b><br>
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(two sides equal,<br>
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two angles equal) </td>
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<td> </td>
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<td><b>Scalene Triangle</b><br>
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(no sides equal,<br>
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no angles equal) </td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger"><b>3</b> Lines of Symmetry</td>
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<td> </td>
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<td class="larger"><b>1</b> Line of Symmetry</td>
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<td> </td>
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<td class="larger"><b>No</b> Lines of Symmetry</td>
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</tr>
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</tbody></table>
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<p>I have collected some more examples at <a href="symmetry-line-plane-shapes.html">Lines of Symmetry of Plane Shapes</a>.</p>
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<p> </p>
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<div class="questions">847, 848, 1786, 1787, 3356, 3357, 3358, 3359</div>
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<div class="related">
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<a href="symmetry.html">Symmetry</a>
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<a href="symmetry-artist.html">Symmetry Artist</a>
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<a href="symmetry-rotational.html">Rotational Symmetry</a>
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<a href="symmetry-point.html">Point Symmetry</a>
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<a href="transformations.html">Transformations</a>
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<a href="reflection.html">Reflection</a>
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<a href="index.html">Geometry Index</a>
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</div>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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