Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 464: 5

Answer

The median of the vertex is perpendicular to the base.

Work Step by Step

We call the top of the triangle the point x, y, and we put one corner of the triangle at the origin. Since it is isosceles, we find the slopes: $m_1 = \frac{0-0}{a-0}=0$ $m_1 = \frac{b-0}{a-a}$=undefined Since one slope is undefined and one slope is vertical, one line is vertical, and the other is horizontal. Thus, the two lines are perpendicular.
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