Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 10 - Review Exercises - Page 486: 36


The midpoints of a trapezoid are connected to form a rhombus.

Work Step by Step

We call the midpoints (b,c), (a,2c), (2a-b,c), and (a,0). Thus, we use the distance formula: $d_1 = \sqrt{(2c-c)^2 + (b-a)^2 } = \sqrt{c^2 + (b-a)^2}$ $d_2 = \sqrt{(2c-c)^2 + (a-2a+b)^2 } = \sqrt{c^2 + (b-a)^2}$ $d_3 = \sqrt{(c-0)^2 + (2a-b-a)^2 } = \sqrt{c^2 + (b-a)^2}$ $d_4 = \sqrt{(c-0)^2 + (b-a)^2 } = \sqrt{c^2 + (b-a)^2}$ The sides all have equal lengths, so the shape is a rhombus.
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