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158 lines
6.0 KiB
HTML
158 lines
6.0 KiB
HTML
<!doctype html>
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<html lang="en">
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<!-- #BeginTemplate "/Templates/Advanced.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/geometry/triangle-centers.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:08 GMT -->
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<head>
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<meta charset="UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Triangle Centers</title>
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<script language="JavaScript" type="text/javascript">reSpell=[["center","centre"],["centers","centres"]];</script>
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<meta name="description" content="Learn about the many centers of a triangle such as Centroid, Circumcenter and more.">
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin>
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<link rel="preload" href="../style4.css" as="style">
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<link rel="preload" href="../main4.js" as="script">
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<link rel="stylesheet" href="../style4.css">
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gtag('config', 'UA-29771508-1');
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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-adv.svg" alt="Math is Fun Advanced"></a></div>
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<div id="search" role="search"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Triangle Centers</h1>
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<p>Where is the center of a triangle?</p>
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<p>There are actually <i>thousands</i> of centers!</p>
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<p>Here are the 4 most popular ones:</p>
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<p class="center"><img src="images/triangle-centers.svg" alt="triangle centers: Centroid, Circumcenter, Incenter and Orthocenter" height="308" width="500" ></p>
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<p class="center">Centroid, Circumcenter, Incenter and Orthocenter</p>
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<p>For each of those, the "center" is where special lines cross, so <b>it all depends on those lines</b>!</p>
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<p>Let's look at each one:</p>
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<h2>Centroid</h2>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td><img src="images/triangle-center-median.svg" alt="triangle center median" height="102" width="175" ></td>
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<td>
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<p>Draw a line (called a "median") from each corner to the midpoint of the opposite side.<br>
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Where all three lines intersect is the <a href="centroid.html">centroid</a>, which is also the "center of mass":</p></td>
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</tr>
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</tbody></table>
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<div class="script" style="height: 290px;">
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images/triangle.js?mode=median
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</div>
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<p>Try this: cut a triangle from cardboard, draw the medians. Do they all meet at one point? Can you balance the triangle at that point?</p>
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<p class="center"><img src="images/centroid-triangle.svg" alt="triangle centers: Centroid, Circumcenter, Incenter and Orthocenter" height="179" width="396" ></p>
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<h2>Circumcenter</h2>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td><img src="images/triangle-center-circumcenter.svg" alt="triangle center circumcenter" height="118" width="177" ></td>
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<td>Draw a line (called a "perpendicular bisector") at right angles to the midpoint of each side.<br>
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Where all three lines intersect is the center of a triangle's "circumcircle", called the "circumcenter":<br>
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</td>
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</tr>
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</tbody></table>
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<div class="script" style="height: 290px;">
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images/triangle.js?mode=circum
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</div>
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<p>Try this: drag the points above until you get a right triangle (just by eye is OK). Where is the circumcenter? Why?</p>
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<h2>Incenter</h2>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td><img src="images/triangle-center-angle-bisector.svg" alt="triangle center angle bisector" height="102" width="222" ></td>
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<td>Draw a line (called the "angle <a href="bisect.html">bisector</a>") from a corner so that it splits the angle in half<br>
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Where all three lines intersect is the center of a triangle's "incircle", called the "incenter":</td>
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</tr>
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</tbody></table>
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<div class="script" style="height: 290px;">
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images/triangle.js?mode=incircle
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</div>
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<p>Try this: find the incenter of a triangle using a compass and straightedge at: <a href="construct-triangleinscribe.html">Inscribe a Circle in a Triangle</a></p>
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<h2>Orthocenter</h2>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td><img src="images/triangle-center-height.svg" alt="triangle center height" height="109" width="164" ></td>
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<td>Draw a line segment (called the "altitude") at right angles to a side that goes to the opposite corner.<br>
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Where all three lines intersect is the "orthocenter":</td>
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</tr>
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</tbody></table>
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<div class="script" style="height: 290px;">
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images/triangle.js?mode=ortho
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</div>
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<p>Note that sometimes the edges of the triangle have to be extended outside the triangle to draw the altitudes. Then the orthocenter is also outside the triangle.</p>
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<p> </p>
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<div class="related">
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<a href="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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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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</div>
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</body>
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