A median of a triangle is a segment connecting a vertex of a triangle to the midpoint of the opposite side. Let T be the triangle with vertices (0, 0), (a, 0), and (c, d). Prove that the centroid of triangle T is two-thirds of the way from each vertex to the opposite side.
A median of a triangle is a segment connecting a vertex of a triangle to the midpoint of the opposite side. Let T be the triangle with vertices (0, 0), (a, 0), and (c, d). Prove that the centroid of triangle T is two-thirds of the way from each vertex to the opposite side.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 20E
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A median of a triangle is a segment connecting a vertex of a triangle to the midpoint of the opposite side. Let T be the triangle with vertices (0, 0), (a, 0), and (c, d).
Prove that the centroid of triangle T is two-thirds of the way from each vertex to the opposite side.
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