Question

Name two pairs of congruent alternate interior angles.

Short answer

The required pairs are $\angle 3\cong \angle 6$and $\angle 4\cong \angle 5$.

Step-by-step solution

Step 1. Determine the theorem or postulate

Theorem 3-2 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are positioned on alternate interior side represents the congruent angles.

Step 2. Determine the alternate interior angles

The angles $\angle 3$and $\angle 6$are positioned on the transversal but these angles are having the opposite sides along with this these angles are representing the non adjacent interior angles. So according to the definition of alternate interior angles which states that angles are alternate interior angles when they are positioned on the transversal but these angles are having the opposite sides along with this these angles are representing the non adjacent interior angles the angles are alternate interior angles.

Also the angles $\angle 4$and $\angle 5$having the same properties of angles $\angle 3$and $\angle 6$which means that these angles are also alternate interior angles.

Step 3. Use the theorem 3-2 and determine the conclusion

Label the provided diagram.

According to the figure the lines l and m are having a parallel connection and a separate line p is travelling through them so according to the theorem 3-2 $\angle 3\cong \angle 6$and $\angle 4\cong \angle 5$.