Question

I need help with this please!

Answer 1

Answer:

If two parallel lines  $p$ and $q$ are cut by a transversal, then the alternate interior angles are congruent.

Below is the prove of this.

Step-by-step explanation:

As we know that Alternate interior angles are two angles that are on the interior of $p$ and $q$, but on opposite sides of the transversal.

In other words,  If two parallel lines  $p$ and $q$ are cut by a transversal, then the alternate interior angles are congruent.

Lets prove this.

Given: p ║ q

Prove: ∠1 ≅ ∠2

Statement                                  Reasons

1. p ║ q                                        1. Given

2. ∠1 ≅ ∠3                                  2. Corresponding Angles Postulate

3. ∠3 ≅ ∠2                                 3. Vertical Angles Congruence Theorem

4. ∠1 ≅ ∠2                                  4. Transitive Property of Congruence