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: 12

Answer

The median is parallel to each base and has a value equal to the average of the bases.

Work Step by Step

We first assign coordinates: $A: 0,0;\\ B: 2b,2c;\\ C: 2d,2c;\\ D: 0,2a$ We find the slope of the segment attaching the midpoints: $m = \frac{c-c}{d-b-a}=0$ Thus, it is parallel to the x-axis, which is parallel to each base. Its length is: $=b+a-d$. The average length of the two bases is: $=\frac{2b-2d+2a}{2} =b+a-d$. Thus, the median is parallel to each base and has a value equal to the average of the bases.
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