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: 21

Answer

$\angle EIG\cong\angle FIH$ $\angle EIF\cong\angle GIH$

Work Step by Step

Theorem 2.4 tells us that right angles are congruent. Both $\angle EIG$ and $\angle FIH$ are marked as right angles. Theorem 2.3, the Congruent Complements Therorem, tells us that angles that are complements of the same angle are congruent. $\angle EIF$ and $\angle GIH$ are both complements of $\angle FIG$.
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