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245 lines
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<title>Lines of Symmetry of Plane Shapes</title>
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<h1 align="center">Lines of Symmetry of Plane Shapes</h1>
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<h2>Line of Symmetry</h2>
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<table border="0" align="center">
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<tr>
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<td><img src="images/flame-mirror.jpg" width="156" height="214" alt="dog mirror" /></td>
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<td valign="top"> </td>
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<td valign="top"><p align="center"> </p>
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<p align="center">Here my dog "Flame" has her face <br>
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made perfectly symmetrical with a bit<br>
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of photo magic.</p>
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<p align="center">The white line down the center is the<br>
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<b>Line of Symmetry</b></p></td>
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</tr>
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</table>
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<div align="center">Read more at <a href="symmetry-reflection.html">Reflection Symmetry</a>. </div>
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<h2>Folding Test</h2>
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<p>You can find if a shape has a Line of Symmetry by<b> folding it</b>. </p>
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<div class="def">
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<p>When the folded part sits perfectly on top (all edges matching), then the fold line is a Line of Symmetry.</p>
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</div>
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<p>Here I have folded a rectangle one way, and <b>it didn't work</b>.</p>
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<p align="center"><img src="images/symmetry-folding-no.svg" alt="symmetry folding no" style="max-width:100%" /><br />
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<span class="larger">So this is <b>not</b> a Line of Symmetry</span></p>
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<p>But when I try it this way, it <b>does work</b> (the folded part sits perfectly on top, all edges matching):</p>
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<p align="center"><img src="images/symmetry-folding-yes.svg" alt="symmetry folding yes" style="max-width:100%" /><br />
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<span class="larger">So this <b>is</b> a Line of Symmetry</span></p>
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<h2>Triangles</h2>
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<p>A <a href="../triangle.html">Triangle</a> can have <b>3</b>, or <b>1</b> or <b>no</b> lines of symmetry:
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</p>
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<table border="0" align="center">
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<tr align="center">
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<td><img src="images/symmetry-equilateral-triangle.gif" width="130" height="130" alt="symmetry equilateral triangle" /></td>
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<td> </td>
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<td><img src="images/symmetry-isosceles-triangle.gif" width="131" height="130" alt="symmetry isosceles triangle" /></td>
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<td> </td>
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<td><img src="images/symmetry-scalene-triangle.gif" width="130" height="130" alt="no symmetry scalene triangle" /></td>
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</tr>
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<tr 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 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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</table>
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<h2>Quadrilaterals </h2>
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<p>Different types of <a href="../quadrilaterals.html">Quadrilaterals</a> (a 4-sided plane shape): </p>
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<table border="0" align="center">
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<tr align="center">
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<td><img src="images/symmetry-square.gif" width="130" height="130" alt="symmetry square" /></td>
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<td> </td>
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<td><img src="images/symmetry-rectangle.gif" width="130" height="130" alt="symmetry rectangle" /></td>
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<td> </td>
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<td><img src="images/symmetry-irregular-quad.gif" width="130" height="130" alt="symmetry irregular quad" /></td>
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</tr>
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<tr align="center">
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<td><b>Square</b><br />
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(all sides equal, <br />
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all angles 90°) </td>
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<td> </td>
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<td><b>Rectangle</b><br />
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(opposite sides equal, <br />
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all angles 90°)</td>
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<td> </td>
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<td><b>Irregular <br />
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Quadrilateral</b><br /></td>
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</tr>
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<tr align="center">
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<td class="larger"><b>4</b> Lines of Symmetry</td>
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<td> </td>
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<td class="larger"><b>2</b> Lines 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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</table>
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<p> </p>
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<table border="0" align="center">
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<tr align="center">
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<td><img src="images/symmetry-kite.gif" width="130" height="130" alt="symmetry kite" /></td>
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<td> </td>
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<td><img src="images/symmetry-rhombus.gif" width="130" height="130" alt="symmetry rhombus" /></td>
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</tr>
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<tr align="center">
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<td><b>Kite</b><br /></td>
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<td> </td>
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<td><b>Rhombus</b><br />
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(all sides equal length) </td>
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</tr>
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<tr align="center">
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<td class="larger"><b>1</b> Line of Symmetry</td>
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<td class="larger"> </td>
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<td class="larger"><b>2</b> Lines of Symmetry</td>
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</tr>
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</table>
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<h2>Regular Polygons</h2>
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<p>A regular <a href="polygons.html">polygon</a> has all sides equal, and all angles equal:</p>
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<table border="0" align="center">
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<tr>
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<td><img src="images/symmetry-equilateral-triangle.gif" width="130" height="130" alt="symmetry equilateral triangle" /></td>
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<td>An <b>Equilateral Triangle</b> (3 sides) <br />
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has <b> 3</b> Lines of Symmetry</td>
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<td> </td>
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</tr>
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<tr>
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<td> </td>
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<td align="right"><img src="images/symmetry-square.gif" width="130" height="130" alt="symmetry square" /></td>
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<td>A <b>Square</b> (4 sides) <br />
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has <b> 4</b> Lines of Symmetry</td>
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</tr>
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<tr>
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<td><img src="images/symmetry-regular-pentagon.gif" width="130" height="130" alt="symmetry regular pentagon" /></td>
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<td>A <b>Regular Pentagon</b> (5 sides) <br />
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has <b> 5</b> Lines of Symmetry</td>
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<td> </td>
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</tr>
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<tr>
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<td> </td>
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<td align="right"><img src="images/symmetry-regular-hexagon.gif" width="130" height="130" alt="symmetry regular hexagon" /></td>
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<td>A <b>Regular Hexagon</b> (6 sides) <br />
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has <b>6</b> Lines of Symmetry</td>
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</tr>
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<tr>
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<td><img src="images/symmetry-regular-septagon.gif" width="130" height="130" alt="symmetry regular septagon" /></td>
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<td>A <b>Regular Heptagon</b> (7 sides) <br />
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has <b> 7</b> Lines of Symmetry</td>
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<td> </td>
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</tr>
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<tr>
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<td> </td>
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<td align="right"><img src="images/symmetry-regular-octagon.gif" width="130" height="130" alt="symmetry regular octagon" /></td>
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<td>A <b>Regular Octagon</b> (8 sides) <br />
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has <b> 8</b> Lines of Symmetry</td>
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</tr>
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</table>
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<p>And the pattern continues: </p>
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<ul>
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<li>A regular polygon of <b>9</b> sides has <b>9</b> Lines of Symmetry</li>
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<li>A regular polygon of <b>10</b> sides has <b>10</b> Lines of Symmetry</li>
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<li>...</li>
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<li>A regular polygon of <b>"n"</b> sides has <b>"n"</b> Lines of Symmetry </li>
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</ul>
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<table border="0">
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<tr>
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<td><h2>Circle</h2>
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<div>
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<div></div>
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</div>
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<p>A line (drawn at any angle) that goes through its center is a Line of Symmetry. </p>
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<p>So a Circle has<b> infinite</b> Lines of Symmetry. </p></td>
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<td> </td>
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<td><img src="images/circle-symmetry.gif" width="132" height="114" alt="circle symmetry" /></td>
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</tr>
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</table>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(2509, 2510, 9003, 9004, 9005, 793, 9165, 9167, 9166, 498);</script>
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</div>
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<div class="related">
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<a href="symmetry-reflection.html">Reflection Symmetry</a>
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<a href="symmetry.html">Symmetry</a>
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<a href="index.html">Geometry Index</a>
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Copyright © 2017 MathsIsFun.com
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