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: 13

Answer

The median is parallel to the base and has half the length of the base.

Work Step by Step

These are similar triangles, for they have three congruent angles. Thus, the median is parallel to the base of the triangle. We call the length of the base 2a, and we call the peak of the triangle $(2b,2c)$. Thus, the median's length is: $=c-a-c=a$. Half of the base is: $=a$. Thus, the median is parallel to the base and has half the length of the base.
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