Question

tv is parallel to wx. cody constructed: - wu perpendicular to tv such that u is on tv - vy perpendicular to wx such that y is on wx cody noticed that △uwv≅△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. Given $\overleftrightarrow{TV}\parallel\overleftrightarrow{WX}$, and $\triangle UWV\cong\triangle YVW$ by Hypotenuse - Leg congruency.
2. In congruent triangles $\triangle UWV$ and $\triangle YVW$, corresponding angles are congruent. The angles formed by the transversal $\overleftrightarrow{WV}$ with the parallel lines $\overleftrightarrow{TV}$ and $\overleftrightarrow{WX}$ are alternate - interior angles.
3. The congruence of these angles proves the theorem that when a transversal crosses parallel lines, alternate - interior angles are congruent.

Answer:

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