Chapter 5.2, Problem 3PSA

To determine

To Find: All the pairs of congruent angles for which the given line is parallel.

Answer to Problem 3PSA

As we know that when parallel lines is intersected by a transversal pairs of Alternate interior angles are congruent.

  $\begin{array}{l}\angle 3\cong \angle 5;\angle 4\cong \angle 6\left(\text{Pairs of alternate interior angles}\right)\\ \angle 1\cong \angle 7;\angle 2\cong \angle 8\left(\text{Pairs of alternate exterior angles}\right)\\ \begin{array}{c}\angle 1\cong \angle 5;\angle 2\cong \angle 6\\ \angle 3\cong \angle 7;\angle 4\cong \angle 8\end{array}\}\left(\text{Pairs of corresponding angles}\right)\\ \begin{array}{c}\angle 1\cong \angle 3;\angle 2\cong \angle 4\\ \angle 5\cong \angle 7;\angle 6\cong \angle 8\end{array}\}\left(\text{Pairs of vertically opposite angles}\right)\end{array}$

Explanation of Solution

Given:

  

Two parallel lines a and b are intersected by a transversal.

Concept Used:

When parallel lines is intersected by a transversal following pairs of angles are congruent:

• Alternate interior angles
• Alternate exterior angles
• Corresponding angles
• Vertically opposite angles

Calculation:

Here, we have two parallel lines a and b are intersected by a transversal.

As we know that when parallel lines is intersected by a transversal pairs of Alternate interior angles are congruent.

  $\Rightarrow \angle 3\cong \angle 5;\angle 4\cong \angle 6$

When parallel lines is intersected by a transversal pairs of Alternate exterior angles are congruent.

  $\Rightarrow \angle 1\cong \angle 7;\angle 2\cong \angle 8$

When parallel lines is intersected by a transversal pairs of corresponding angles are congruent.

  $\begin{array}{l}\Rightarrow \angle 1\cong \angle 5;\angle 2\cong \angle 6\\ \angle 3\cong \angle 7;\angle 4\cong \angle 8\end{array}$

When parallel lines is intersected by a transversal pairs of vertically opposite angles are congruent.

  $\begin{array}{l}\Rightarrow \angle 1\cong \angle 3;\angle 2\cong \angle 4\\ \angle 5\cong \angle 7;\angle 6\cong \angle 8\end{array}$