Question

Karen knows that when two parallel lines are cut by a transversal, alternate interior angles are congruent and vertical angles are congruent. Which of these can she prove, and how?

A) She can prove that alternate exterior angles are supplementary by using the Transitive Property.
B) She can prove that alternate exterior angles are congruent by using the Transitive Property.
C) She can prove that alternate exterior angles are supplementary by using the Symmetric Property.
D) She can prove that alternate exterior angles are congruent by using the Symmetric Property.

Answer 1

Karen can prove that alternate exterior angles are congruent by using the Transitive Property.

Step-by-step explanation:

Karen can prove that alternate exterior angles are congruent by leveraging the Transitive Property. In the context of parallel lines intersected by a transversal, she recognizes the congruence of alternate interior angles. As these angles are supplementary to the same interior angles on the same side of the transversal, they are inherently congruent. By applying the Transitive Property, which asserts that if two angles are congruent to a third angle, then they are congruent to each other, Karen logically establishes the congruence of alternate exterior angles. This approach succinctly demonstrates the validity of her proof in justifying angle relationships.