Question

cody noticed that $\triangle uwv \cong \triangle yvw$ using the hypotenuse-leg congruency postulate.
what theorem can cody prove using these congruent triangles?
choose 1 answer:
a when a transversal crosses parallel lines, alternate interior angles are congruent.
b when a transversal crosses parallel lines, same-side interior angles are congruent.
c angles that form a linear pair are supplementary.
d vertical angles are congruent.

Explanation:

1. Analyze Option A: When a transversal crosses parallel lines, alternate interior angles are congruent. If we have congruent triangles (from Hypotenuse - Leg), we can show corresponding angles are congruent. In the context of parallel lines cut by a transversal, alternate interior angles can be shown congruent by using congruent triangles (e.g., by proving the triangles formed have congruent angles which correspond to alternate interior angles).
2. Analyze Option B: Same - side interior angles are supplementary, not congruent, so this option is incorrect.
3. Analyze Option C: Angles forming a linear pair being supplementary is about adjacent angles on a straight line, not related to congruent triangles from Hypotenuse - Leg postulate for parallel lines.
4. Analyze Option D: Vertical angles being congruent is about angles opposite each other when two lines intersect, not related to parallel lines and the given congruent triangles.

Answer:

A. When a transversal crosses parallel lines, alternate interior angles are congruent.