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.
