Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-6 Proving Angles Congruent - Practice and Problem-Solving Exercises: 24

Answer

Theorem 2.2

Work Step by Step

Theorem 2.2, the Congrent Supplement Theorem, tells is that if two angles are supplements of congruent angles, then those two angles are congruent. $\angle1$ and $\angle3$ are supplementary because they form a linear pair. $\angle2$ and $\angle4$ are supplementary because they form a linear pair. Since $\angle1\cong\angle2$, Theorem 2.2 tells us that $\angle3\cong\angle4$.
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