Geometry: Common Core (15th Edition)

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

Chapter 2 - Reasoning and Proof - Chapter Review: 38

Answer

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \angle1\text{ and }\angle2\text{ are complementary} & \text{Given} \\2 & \angle3\text{ and }\angle4\text{ are complementary} & \text{Given} \\3 & \angle2\cong\angle4 & \text{Given} \\4 & m\angle2=m\angle4 & \text{definition of congruent} \\5 & m\angle1+m\angle2=90 & \text{definition of complementary} \\6 & m\angle3+m\angle4=90 & \text{definition of complementary} \\7 & m\angle1+m\angle2=m\angle3+m\angle4 & \text{transitive property of equality} \\8 & m\angle1+m\angle2=m\angle3+m\angle2 & \text{substitution} \\9 & m\angle1=m\angle3 & \text{subtraction property of equality} \\10 & \angle1\cong\angle3 & \text{definition of congruent} \end{array}

Work Step by Step

Use the given information along with known properties and theorems to prove the statement.
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