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: 30

Answer

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \angle1\text{ and} \angle2\text{ are supplementary} & \text{Given} \\2 & m\angle1+m\angle2=180 & \text{Definition of Supplementary} \\3 & \angle3\text{ and} \angle4\text{ are supplementary} & \text{Given} \\4 & m\angle3+m\angle4=180 & \text{Definition of Supplementary} \\5& m\angle1+m\angle2=m\angle3+m\angle4 & \text{Transitive Property of Equality} \\6 & \angle2\cong\angle4 & \text{Given} \\7 & m\angle2=m\angle4 & \text{Definition of Congruent} \\8 & m\angle1+m\angle4=m\angle3+m\angle4 & \text{Substitution Property of Equality} \\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 definitions of supplementary and of congruent, along with the properties of equality, to write the proof.
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