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153 lines
6.0 KiB
HTML
153 lines
6.0 KiB
HTML
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<title>Complementary Angles</title>
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<h1 class="center">Complementary Angles</h1>
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<p class="center larger">Two angles are Complementary when they <b><br>
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add up to 90 degrees</b> (a Right Angle <span style="vertical-align:middle"><img src="images/symbol-right-angle.svg" alt="right angle" height="" width=""></span>)</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/complementary-angles.svg" alt="complementary angles 40 and 50" height="131" width="137"></p>
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<p> </p>
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<p>These two angles (40° and 50°) are <b>Complementary Angles</b>, because they add up to 90°:</p>
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<p>Notice that together they make a <a href="../rightangle.html">right angle</a> <img src="images/symbol-right-angle.svg" alt="right angle" height="" width=""></p>
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<div style="clear:both"></div>
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<p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"> </p>
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<span style="float:left; margin: 0 10px 5px 0;"><img src="images/complementary-angles2.svg" alt="complementary angles 27 and 63" height="148" width="230"></span>
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<p>But the angles don't have to be together.</p>
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<p>These two are complementary because 27° + 63° = 90°</p>
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<div style="clear:both"></div>
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<h2>Play With It ...</h2>
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<p>(Drag the points)</p>
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images/geom-comp-supp.js?mode=comp
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</div>
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<p> </p>
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<div class="center80">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/triangle-right-angles.svg" alt="complementary right angle triangle 22 and 68" height="93" width="237"></p>
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<h3>Right Angled Triangle</h3>
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<p>In a right angled triangle, the two non-right angles are complementary, because in a triangle <a href="../proof180deg.html">the three angles add to 180°</a>, and 90° has already been taken by the right angle.</p>
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</div>
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<p> </p>
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<p class="words">When two angles add to 90°, we say they <b>"Complement"</b> each other.<br>
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<b><br>Complementary</b> comes from Latin <i>completum</i> meaning "completed" ...<br>
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because the right angle is thought of as being a complete angle.</p><p class="info"><i>Spelling:</i> be careful, it is <i><b>not</b></i> <i>"Complimentary Angle"</i> (with an "i") ...<br>
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that would be an angle you get for free!</p>
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<h2>Complementary vs Supplementary</h2>
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<p>A related idea is <a href="supplementary-angles.html">Supplementary Angles</a> - those add up to 180°</p>
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<div class="center80">
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<p>How to remember which is which? Well, <b>alphabetically</b> they are:</p>
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<ul>
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<li>Complementary add to 90°</li>
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<li>Supplementary add to 180°</li>
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</ul>
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<p>You can also think:</p>
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<ul>
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<li>"<b>C</b>" of <b>C</b>omplementary is for "<b>C</b>orner" <img src="images/symbol-right-angle.svg" alt="right angle" height="" width="">(a Right Angle), and</li>
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<li>"<b>S</b>" of <b>S</b>upplementary is for "<b>S</b>traight" (180° is a straight line)</li>
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</ul>
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<p>Or you can think:</p>
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<ul>
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<li>when you are <b>right</b> you get a <b>compliment</b> (sounds like compl<b>e</b>ment)</li>
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<li>"supplement" (like a vitamin supplement) is something extra, so is bigger</li>
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</ul>
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</div>
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<p> </p>
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<p> </p>
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<div class="questions">5231, 5233, 819, 2109, 820, 2110, 5240, 9063, 3305, 3306</div>
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<div class="related">
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<a href="supplementary-angles.html">Supplementary Angles</a>
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<a href="symbols.html">Symbols in Geometry</a>
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<a href="degrees.html">Degrees (Angle)</a>
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<a href="../angle180.html">Angles On a Straight Line</a>
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<a href="../angle360.html">Angles Around a Point</a>
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<a href="parallel-lines.html">Parallel Lines and Pairs of Angles</a>
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<a href="interior-angles.html">Interior Angles</a>
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<a href="index.html">Geometry Index</a>
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</div>
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</article>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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