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111 lines
5.7 KiB
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111 lines
5.7 KiB
HTML
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<title>Exterior Angle Theorem</title>
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<h1 class="center">Exterior Angle Theorem</h1>
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<p>For a triangle: </p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/exterior-angle-theorem.gif" width="249" height="78" alt="exterior angle theorem d = a+b, d>a, d>b" /></p>
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<ul>
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<li>The exterior angle <b>d</b> equals the angles <b>a plus b</b>.</li>
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<li>The exterior angle <b>d</b> is greater than angle <b>a</b>, or angle <b>b</b>.</li>
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</ul>
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<p> </p>
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<h3>Example: </h3>
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<p class="center"><img src="images/exterior-angle-theorem-b.gif" width="275" height="81" alt="exterior angle theorem 35+62=97" /></p>
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<p class="center">The exterior angle is <b>35° + 62° = 97°</b></p>
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<p class="center">And <b>97°</b> > <b>35°</b></p>
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<p class="center">And <b>97°</b> > <b>62°</b></p>
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<h2>Why? </h2>
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<p>Because the<a href="../proof180deg.html"> interior angles of a triangle add to 180°</a>, and angles c+d also add to 180°:</p>
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<p class="center"><img src="images/exterior-angle-theorem-c.gif" width="302" height="81" alt="exterior angle theorem triangle a+b+c=180, c+d=180" /></p>
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<div class="tbl">
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<div class="row"><span class="left">The interior angles of a triangle add to 180°:</span><span class="right">a + b + c = 180°</span></div>
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<div class="row"><span class="left">Angles <b>c</b> and <b>d</b> make a straight angle, which is 180°:</span><span class="right">d + c = 180°</span></div>
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<div class="row"><span class="left">So <b>d + c</b> equals <b>a + b + c</b>:</span><span class="right">d + c = a + b + c</span></div>
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<div class="row"><span class="left">Subtract <b>c</b> from both sides:</span><span class="right">d = a + b</span></div>
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</div>
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<h2>Works For Any Triangle's Exterior Angle</h2>
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<div class="example">
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<h3>Example: </h3>
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<p class="center"><img src="images/exterior-angle-theorem-d.gif" width="184" height="86" alt="exterior angle theorem 27 and 40 inside triangle, 67 outside" /></p>
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<p class="center">The exterior angle is <b>40° + 27° = 67°</b></p>
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<p class="center">And <b>67°</b> > <b>40°</b></p>
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<p class="center">And <b>67°</b> > <b>27°</b></p>
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</div>
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<div class="example">
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<h3>Example: How big is angle <b>d</b>?</h3>
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<p class="center"><img src="images/exterior-angle-theorem-e.gif" width="150" height="132" alt="exterior angle theorem 61 inside triangle, d outside" /></p>
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<p class="center">We can't calculate exactly, but we <b>can</b> say:<b></b></p>
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<p class="center"><b>d°</b> > <b>61°</b></p>
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</div>
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<p> </p>
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<div class="related"><a href="../proof180deg.html">The Three Angles Add to 180°</a>
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<a href="index.html">Geometry Index</a>
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