Final answer:
Using the Alternate Interior Angles Theorem, ∠BAG and ∠ABH are proven congruent because they are alternate interior angles formed by transversal t intersecting parallel lines a and b.
Step-by-step explanation:
To prove that alternate interior angles ∠BAG and ∠ABH are congruent when transversal t intersects parallel lines a and b, we can use the Alternate Interior Angles Theorem. This theorem states that when a transversal crosses parallel lines, alternate interior angles are equal in measure. Since a and b are parallel, and line t is a transversal, it follows that ∠BAG and ∠ABH are indeed congruent.
By this theorem, we understand that each pair of alternate interior angles are equal because the lines are parallel and the transversal imposes equal, alternate angles. In the case of ∠BAG and ∠ABH, they are on opposite sides of the transversal t, but between the parallel lines a and b, hence they are congruent.