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: 25

Answer

If the angles are congruent and sum to 180, then each measures half of 180, or 90. By definition an angle that measures 90 is a right angle, so both are right angles.

Work Step by Step

By the definition of congruent, $m\angle ABC=m\angle XYZ$. $m\angle ABC+m\angle XYZ=180\longrightarrow$ is given $m\angle ABC+m\angle ABC=180\longrightarrow$ substitution $2m\angle ABC=180\longrightarrow$ combine like terms $m\angle ABC =90\longrightarrow$ division property of equality $m\angle XYZ=90\longrightarrow$ transitive property of equality
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