A transversal intersects two lines. Which conditions would always make the two lines parallel?

A) Vertical Angles are Congruent
B) Alternate interior angles are congruent
C) Corresponding angles are supplementary
D) Same-side interior angles are complementary
I chose c

I researched and got b as the answer. Is that correct?

a little more research ...

a b d

Nthing

To determine which conditions would always make the two lines parallel, we need to recall the properties of transversals and the relationships between angles formed when a transversal intersects two lines.

Option A states that vertical angles are congruent. Vertical angles are formed by two intersecting lines, across from each other. While vertical angles being congruent provides useful information, it does not guarantee that the lines are parallel. So, we can eliminate option A.

Option B states that alternate interior angles are congruent. Alternate interior angles are formed on opposite sides of the transversal, between the two lines. If the alternate interior angles are congruent, it is a sufficient condition to prove that the two lines are parallel. Therefore, option B is correct.

Option C states that corresponding angles are supplementary. Corresponding angles are formed on the same side of the transversal and in corresponding positions in relation to the two lines. While corresponding angles being supplementary is a property of parallel lines, it is not a guarantee. Two lines can have supplementary corresponding angles and still not be parallel. So, we can eliminate option C.

Option D states that same-side interior angles are complementary. Same-side interior angles are formed on the same side of the transversal, between the two lines. If same-side interior angles are complementary, i.e., their measures add up to 90 degrees, it is not a guarantee that the lines are parallel. So, we can eliminate option D.

Therefore, the correct answer is option B: alternate interior angles being congruent.