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.
