Question

in the picture below, line pq is parallel to line rs, and the lines are cut by a transversal, line tu. the transversal is not perpendicular to the parallel lines. note: figure is not drawn to scale. which of the following are congruent angles? a. $\angle y \cong \angle e$ b. $\angle h \cong \angle g$ c. $\angle z \cong \angle h$ d. $\angle y \cong \angle h$

Explanation:

To determine congruent angles when parallel lines are cut by a transversal, we use angle - related theorems (corresponding angles, alternate interior angles, vertical angles, etc.).

• For option A: $\angle Y$ and $\angle E$ do not have a relationship (corresponding, alternate interior, vertical, etc.) that would make them congruent.
• For option B: $\angle H$ and $\angle G$ are adjacent angles and are supplementary (they form a linear pair), not congruent.
• For option C: $\angle Z$ and $\angle H$ are not related by any of the angle - congruence theorems for parallel lines cut by a transversal.
• For option D: $\angle Y$ and $\angle H$ are corresponding angles. When two parallel lines (PQ and RS) are cut by a transversal (TU), corresponding angles are congruent. So $\angle Y\cong\angle H$.

Answer:

D. $\angle Y\cong\angle H$