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Mathematics LibreTexts

2.C: Bisectors, Medians, and Altitudes

  • Page ID
    31443
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    Overview

    The purpose of this lesson is to identify the different "centers" of a triangle.

    This lesson will address the following CCRS Standard(s) for Geometry:

    • 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

    Directions

    1. Take notes while watching videos below
    2. Go to http://wamap.org and log into our course to complete assignment 2.C with 80% or better.

    Do

    Complete assignment 2.C with 80% or better at http://wamap.org

    Summary

    In this lesson we have learned:

    • A perpendicular bisector cuts a line segment in half forming a right angle
      • All three perpendicular bisectors of a triangle meet at the circumcenter
      • The circumcenter is equidistant to each of the vertices of the triangle
      • The circumcenter is the center of the circle around the triangle
    • An angle bisector cuts an angle into two congruent halves
      • All three angle bisectors of a triangle meet at the incenter
      • The incenter is a point equidistant from each side of the triangle
      • The incenter is the center of the circle inside the triangle
    • A median connects the middle of one of the triangle sides to the vertex opposite the segment
      • All three medians of a triangle meet at the centroid
      • The centroid is the point of balance for the triangle
      • The centroid is 2/3 the distance from each vertex to the midpoint of the opposite side
    • An altitude connects a vertex to the opposite side of the triangle, forming a right angle
      • All three altitudes of a triangle meet at the orthocenter
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