Chapter 5.3, Problem 11PSA

To determine

To Find: All the pairs of angles that are congruent.

Answer to Problem 11PSA

  $\begin{array}{l}\Rightarrow \angle 1\cong \angle 4\\ \Rightarrow \angle 2\cong \angle 5\\ \Rightarrow \angle 3\cong \angle 6\end{array}$

Explanation of Solution

Given:

  

  $\overline{AD}\parallel \overline{BC}$

Concept Used:

If two lines are parallel intersected by a transversal alternate interior angles and opposite angles are equal.

Calculation:

Here, we have

  

  $\overline{AD}\parallel \overline{BC}$

  $\begin{array}{l}\Rightarrow \angle 1\cong \angle 4\left(\text{Opposite angles}\right)\\ \Rightarrow \angle 2\cong \angle 5\left(\text{Alternate interior angles}\right)\\ \Rightarrow \angle 3\cong \angle 6\left(\text{Alternate interior angles}\right)\end{array}$