Elementary Geometry for College Students (5th Edition)

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

Chapter 4 - Section 4.1 - Properties of a Parallelogram - Exercises: 32a

Answer

$\triangle$DEC is a right triangle.

Work Step by Step

Being a parallelogram, $\angle$ADC and $\angle$BCD are supplementary, meaning they add up to 180$^{\circ}$. Each of these angles have been bisected to create $\angle$EDC and $\angle$ECD. Bisected means cut in half, and half of 180$^{\circ}$ is 90$^{\circ}$, which makes these two angles complementary (adding up to 90$^{\circ}$) The sum of the angles of a triangle is 180$^{\circ}$. 180$^{\circ}$ - 90$^{\circ}$ = 90$^{\circ}$, so the remaining $\angle$DEC is 90$^{\circ}$, making $\triangle$DEC a right triangle.
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