<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <title>2.C: Bisectors, Medians, and Altitudes</title> <meta name="identifier" content="ibdc7498dcae342f4791f59be78890afa"/> <meta name="editing_roles" content="teachers"/> <meta name="workflow_state" content="active"/> </head> <body> <div id="HS21"> <div class="overview"> <h2>Overview</h2> <p>The purpose of this lesson is to identify the different "centers" of a triangle.</p> <p>This lesson will address the following CCRS Standard(s) for Geometry:</p> <ul> <li><em>8.5.G: Use informal arguments to establish facts about the angle sum and exterior angles of triangles, above the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so</em></li> </ul> </div> <div class="directions"> <h2>Directions</h2> <ol> <li>Take notes while watching videos below</li> <li>Go to <a class="external" href="http://wamap.org/" target="_blank">http://wamap.org</a> and log into our course to complete assignment 2.CÂ with 80% or better.</li> </ol> </div> <h3>Watch</h3> <p><a class="" href="https://youtu.be/SIkRwXslAgw">Bisectors, Medians, and Altitudes [7:51]</a></p> <h3>Do</h3> <p>Complete assignment 2.C with 80% or better at <a href="http://wamap.org">http://wamap.org</a></p> <div class="summary"> <h2>Summary</h2> <p>In this lesson we have learned:</p> <ul> <li>A perpendicular bisector cuts a line segment in half forming a right angle <ul> <li>All three perpendicular bisectors of a triangle meet at the circumcenter</li> <li>The circumcenter is equidistant to each of the vertices of the triangle</li> <li>The circumcenter is the center of the circle around the triangle</li> </ul> </li> <li>An angle bisector cuts an angle into two congruent halves <ul> <li>All three angle bisectors of a triangle meet at the incenter</li> <li>The incenter is a point equidistant from each side of the triangle</li> <li>The incenter is the center of the circle inside the triangle</li> </ul> </li> <li>A median connects the middle of one of the triangle sides to the vertex opposite the segment <ul> <li>All three medians of a triangle meet at the centroid</li> <li>The centroid is the point of balance for the triangle</li> <li>The centroid is 2/3 the distance from each vertex to the midpoint of the opposite side</li> </ul> </li> <li>An altitude connects a vertex to the opposite side of the triangle, forming a right angle <ul> <li>All three altitudes of a triangle meet at the orthocenter</li> </ul> </li> </ul> </div> </div> </body> </html>