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? - Page 123: 3


$\angle1$ and $\angle3$ are vertical angles because it is given. $\angle1$ and $\angle2$ are supplementary by the definition of a linear pair. $\angle2$ and $\angle3$ are also supplementary by the definition of a linear pair. By the definition of supplementary, $m\angle1+m\angle2=180$ and $m\angle2+m\angle3=180$. By the Transitive Property of Equality, $m\angle1+m\angle2=m\angle2+m\angle3.$ By the Subtraction Property of Equality $m\angle1=m\angle3.$ $\angle1\cong\angle2$ because angles with the same measure are congruent.

Work Step by Step

To write a paragraph proof, Convert each row of statements and reasons into sentences.
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