Chapter 3, Problem 10STP

To determine

To complete: The proof table.

Answer to Problem 10STP

Vertically opposite angle

Explanation of Solution

Given: $\angle 1\cong \angle 2$ and to prove $a\left|\right|b$

  

The proof table.

  $\begin{array}{cc}\text{Statements}& \text{Reasons}\\ \begin{array}{cc}1.& \angle 1\cong \angle 2\end{array}& \begin{array}{cc}1.& \text{Given}\end{array}\\ \begin{array}{cc}2.& \angle 2\cong \angle 3\end{array}& \begin{array}{cc}2.& \text{Vertically opposite angles}\end{array}\\ \begin{array}{cc}3.& \angle 1\cong \angle 3\end{array}& \begin{array}{cc}3.& \text{Transitive}\end{array}\\ \begin{array}{cc}4.& a\left|\right|b\end{array}& \begin{array}{cc}4.& \begin{array}{l}\text{If corresponding}\\ \text{angles are congruent}\\ \text{then the lines are parallel}\text{.}\end{array}\end{array}\end{array}$

So, correct fill is vertically opposite angle.