Question

use the figures to determine whether the indicated lines are parallel. indicate why or why not. ... e) are y and z parallel lines? why or why not? a. yes, because alternate exterior angles are congruent. b. no, because corresponding angles are 155° each c. yes, because vertical angles are complementary. d. no, because a triangle fits between y and z.

Explanation:

To determine if lines \( y \) and \( z \) are parallel, we analyze the angles formed by the transversal. The angle of \( 155^\circ \) on line \( y \) and the \( 155^\circ \) angle on line \( z \) are alternate exterior angles. By the Alternate Exterior Angles Theorem, if alternate exterior angles are congruent, the lines are parallel. Here, the alternate exterior angles are both \( 155^\circ \), so they are congruent, meaning \( y \) and \( z \) are parallel. Option A correctly states this reasoning. Option B is incorrect because congruent corresponding (or alternate exterior) angles imply parallel lines. Option C is incorrect as vertical angles being complementary is not relevant here. Option D is incorrect as the triangle does not affect the parallelism based on angle relationships.

Answer:

A. Yes, because alternate exterior angles are congruent.