Answer:
If two parallel lines
and
are cut by a transversal, then the alternate interior angles are congruent.
Below is the prove of this.
Explanation:
As we know that Alternate interior angles are two angles that are on the interior of
and
, but on opposite sides of the transversal.
In other words, If two parallel lines
and
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