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: 8

Answer

The segments that connect midpoints for a quadrilateral bisect.

Work Step by Step

We assign coordinates for each point on quadrilateral ABCD: $A: 0,0 \\ B: 2a, 2b \\ C: 2c, 2d \\ D: 2e, 0$ This means that the midpoints are: $(a,b); (a+c, b+d); (e,0); (e+c, d)$ We find the midpoint of each line: $mid_1 = (\frac{a+e+c}{2}, \frac{b+d}{2})$ $mid_2 = (\frac{a+e+c}{2}, \frac{b+d}{2})$ The midpoints are the same, so they bisect each other.
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