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267 lines
9.7 KiB
HTML
267 lines
9.7 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/triangle.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:28 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Triangles - Equilateral, Isosceles and Scalene</title>
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<meta name="description" content="A triangle has three straight sides ...">
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<script src="geometry/images/geom-triangle.js" type="text/javascript"></script>
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</script>
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</head>
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="search" role="search"></div>
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<div id="menuSlim" class="menu"></div>
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<div id="menuTiny" class="menu"></div>
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</nav>
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<div id="extra"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<div class="video">c2ZWPA3kduw</div>
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<h1 class="center">Triangles</h1>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="geometry/images/triangle-angles.svg" alt="Triangle with angles" height="83" width="143"></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/style/right-arrow.gif" alt="right arrow" height="46" width="46"> </td>
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<td> </td>
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<td>
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<p class="large">A triangle has three sides and three angles</p></td>
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</tr>
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<tr>
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<td><img src="images/style/right-arrow.gif" alt="right arrow" height="46" width="46"></td>
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<td> </td>
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<td>
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<p class="large">The three angles always add to 180°</p></td>
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</tr>
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</tbody></table>
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<h2>Equilateral, Isosceles and Scalene</h2>
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<p>There are three special names given to triangles that tell how many sides (or angles) are equal.<br>
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<br>
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There can be <b>3</b>, <b>2</b> or <b>no</b> equal sides/angles:</p>
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<div class="simple">
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<table align="center" cellspacing="5" cellpadding="5" border="1">
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<tbody>
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<tr>
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<td style="text-align:center;"><img src="geometry/images/triangle-equilateral.svg" alt="Equilateral Triangle" height="96" width="111"></td>
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<td>
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<h3>Equilateral Triangle</h3>
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<p><b>Three</b> equal sides<br>
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<b>Three</b> equal angles, always 60°</p></td>
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</tr>
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<tr>
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<td style="text-align:center;"><img src="geometry/images/triangle-isosceles.svg" alt="Isosceles Triangle" height="111" width="98"></td>
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<td>
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<h3>Isosceles Triangle</h3>
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<p><b>Two</b> equal sides<br>
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<b>Two</b> equal angles</p></td>
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</tr>
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<tr>
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<td style="text-align:center;"><img src="geometry/images/triangle-scalene.svg" alt="Scalene Triangle" height="61" width="106"></td>
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<td>
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<h3>Scalene Triangle</h3>
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<p><b>No</b> equal sides<br>
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<b>No</b> equal angles</p></td>
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</tr>
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</tbody></table><br>
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</div>
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<p><b>How to remember?</b> Alphabetically they go 3, 2, none:</p>
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<ul>
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<li><b>Equilateral</b>: <b>"equal"</b>-lateral (lateral means side) so they have all <b>equal sides</b></li>
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<li><b>Isosceles</b>: means "equal legs", and we have <b>two legs</b>, right? Also i<b>SOS</b>celes has two equal <b>"S</b>ides" joined by an "<b>O</b>dd" side.</li>
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<li><b>Scalene</b>: means "uneven" or "odd", so no equal sides.</li>
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</ul>
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<h2>What Type of Angle?</h2>
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<p>Triangles can also have names that tell you what <b>type of angle</b> is inside<i>:</i></p>
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<div class="simple">
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<table align="center" cellspacing="5" cellpadding="5" border="1">
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<tbody>
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<tr>
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<td><img src="geometry/images/triangle-acute.svg" alt="Acute Triangle" height="66" width="108"></td>
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<td>
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<h3>Acute Triangle</h3>
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<p>All angles are less than 90°</p></td>
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</tr>
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<tr>
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<td><img src="geometry/images/triangle-right.svg" alt="Right Triangle" height="66" width="108"></td>
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<td>
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<h3>Right Triangle</h3>
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<p>Has a right angle (90°)</p></td>
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</tr>
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<tr>
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<td><img src="geometry/images/triangle-obtuse.svg" alt="Obtuse Triangle" height="67" width="116"></td>
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<td>
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<h3>Obtuse Triangle</h3>
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<p>Has an angle more than 90°</p></td>
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</tr>
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</tbody></table><br>
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</div>
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<h2>Combining the Names</h2>
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Sometimes a triangle will have two names, for example:<br>
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<div class="beach">
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<table align="center" cellspacing="5" cellpadding="5" border="1">
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<tbody>
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<tr>
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<td><img src="geometry/images/triangle-right-isosceles.svg" alt="Right Isosceles Triangle" height="95" width="95"></td>
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<td>
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<h3>Right Isosceles Triangle</h3>
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<p>Has a right angle (90°), and also two equal angles<br>
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<br>
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Can you guess what the equal angles are?</p></td>
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</tr>
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</tbody></table></div>
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<h2>Play With It ...</h2>
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<p>Try dragging the points around and make different triangles:</p>
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<div class="script" style="height: 290px;">
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geometry/images/triangle.js?mode=type
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</div>
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<p>You might also like to play with the <a href="geometry/triangles-interactive.html">Interactive Triangle</a>.</p>
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<h2>Angles</h2>
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<p>The three interior angles always add to 180°</p>
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<div class="script" style="height: 290px;">
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geometry/images/triangle.js?mode=angles
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</div>
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<h2>Perimeter</h2>
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<p>The perimeter is the distance around the edge of the triangle: just add up the three sides:</p>
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<div class="script" style="height: 290px;">
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geometry/images/triangle.js?mode=perim
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</div>
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<h2>Area</h2>
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<p style="float:right; margin: 0 0 5px 10px;"> </p>
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<span style="float:right; margin: 0 0 5px 10px;"><img src="geometry/images/triangle-b-h.svg" alt="triangle base=b height=h" height="137" width="177"></span>
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<p>The area is <b>half of the base times height</b>.</p>
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<ul>
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<li>"b" is the distance along the base</li>
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<li>"h" is the height (measured at right angles to the base)</li>
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</ul>
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<p class="center large">Area = ½ × b × h</p>
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<p>The formula works for all triangles.</p>
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<p>Note: a simpler way of writing the formula is <b class="large">bh/2</b></p>
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<div class="example">
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<h3>Example: What is the area of this triangle?</h3>
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<p class="center"><img src="geometry/images/triangle-area-example.svg" alt="Triangle height=12, base=20" height="135" width="217"></p>
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<p class="center"><i>(Note: 12 is the <b>height</b>, not the length of the left-hand side)</i></p>
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<p class="center"> </p>
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<p class="center">Height = h = 12</p>
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<p class="center">Base = b = 20</p>
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<p class="center larger">Area = ½ × b × h = ½ × 20 × 12 = <b>120</b></p>
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</div>
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<p>The base can be any side, Just be sure the <b>"height" is measured at right angles to the "base"</b>:</p>
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<div class="script" style="height: 290px;">
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geometry/images/triangle.js?mode=area
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</div>
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<p>(Note: You can also calculate the area from the lengths of all three sides using <a href="geometry/herons-formula.html">Heron's Formula</a>.)</p>
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<p> </p>
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<div class="fun">
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<h3>Why is the Area "Half of bh"?</h3>
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<p>Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (a <a href="geometry/parallelogram.html">parallelogram</a>) which can be changed to a simple <a href="quadrilaterals.html">rectangle</a>:</p>
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<p class="center"><img src="geometry/images/triangle-area.svg" alt="triangle area" style="max-width:100%" height="244" width="542"></p>
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<p class="center">THEN the whole area is <b>bh</b>, which is for both triangles, so just one is <b>½ × bh</b>.</p>
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</div>
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<p> </p>
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<div class="questions">6702, 6708,720, 3134, 5032,627,723, 3132, 3133, 7502</div>
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<div class="related">
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<a href="geometry/triangles-interactive.html">Interactive Triangles</a>
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<a href="right_angle_triangle.html">Right Angled triangles</a>
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<a href="proof180deg.html">Proof that a Triangle has 180°</a>
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<a href="pythagoras.html">Pythagoras' Theorem</a>
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<a href="geometry/index.html">Geometry Index</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<div id="adend" class="centerfull noprint"></div>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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