Chapter 5.2, Problem 6PSA

To determine

To Prove: $\angle 1\cancel{\cong }\angle 2$ .

Explanation of Solution

Given:

  

  $\overleftrightarrow{QD}\cancel{\parallel }\overleftrightarrow{UA}$

Concept Used:

When parallel lines is intersected by a transversal alternate interior angles are equal.

Proof:

Here, we have

  $\begin{array}{l}\angle 1\text{and }\angle 2\text{alternate interior angles }\\ \text{Also }\overleftrightarrow{QD}\cancel{\parallel }\overleftrightarrow{UA}\\ \text{Since, we know that when parallel lines is intersected by a transversal alternate interior angles are equal}\text{.}\\ \Rightarrow \angle 1\cancel{\cong }\angle 2\end{array}$