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 - Got It?: 2

Answer

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \angle1\cong\angle2 & \text{Given} \\2 & \angle1\cong\angle3 & \text{Vertical Angles are Congruent} \\3 & \angle2\cong\angle3 & \text{Transitive Property of Congruence} \\4 & \angle2\cong\angle4 & \text{Vertical Angles are Congruent} \\5 & \angle1\cong\angle2\cong\angle3\cong\angle4 & \text{Transitive Property of Congruence} \end{array}

Work Step by Step

You could also use the definition of a linear pair to prove all the angles are congruent. $\angle1$ and $\angle2$ are a linear pair and are congruent, so must measure 90. You can use the definition of a linear pair to prove that all 4 angles have a measure of 90, so all are congruent.
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