Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 480: 18

Answer

A parallelogram is formed.

Work Step by Step

We assign points to each of the midpoints: $A: a,0 \\ B: b,c \\ C: a+2b, 2c \\ D: 2a+b,c$ We now find the slopes of the lines between the midpoints: $m_1 = \frac{c}{b-a}$ $m_2 = \frac{c}{b+a} $ $m_3 = \frac{c}{b-a} $ $m_4= \frac{c}{b+a} $ Since opposite sides are parallel, we see that it is a parallelogram.
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