Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 472: 2


For parallelograms, opposite sides have equal lengths.

Work Step by Step

We place the parallelogram at the origin. We call its coordinates: $A: 0,0 \\ B: b,c \\ C: a+b, c \\ D: a, 0$ Thus, we compare the lengths of opposite sides: $l_1= a $ $l_2=a+b-b =a$ $l_3 = \sqrt{c^2 + b^2}$ $l_4 = \sqrt{b^2 +c^2}$ We see that the lengths of opposite sides are equal.
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