Question

Given: Line segment WZ is congruent to line segment YZ. Line segment WX is parallel to line segment ZY
Prove: triangle WXZ is congruent to triangle YZX.

Answer 1

In your problem where states the given that a line segment Wz is congruent to line YZ. The line segment  WX is parallel to line segment ZY so the ask of the problems is to prove that WXZ is congruent triangle to triangle YZX nad the reason that prove that both angle is congruent is the the given where WZ and ZY is congruent so the both have the same size and the WX is parallel to ZY so it means that they are also, form that reason itself proves that both triangle are equal.

Answer 2

Answer:

According to the hypothesis, both triangles shares XZ as one side in common. Similarly, by hypothesis we know that side WZ is congruent with YZ. So, until now, we have two congruent sides, we just need one more side congruent, or two corresponding angles congruent to demonstrate the congruence between triangles.

By hypothesis, side WX and ZY are parallel, and the side WZ is transversal to them, which forms alternate internal angles, which are congruent. Specifically, according to the parallels and the transversal, angle WXZ is congruent to YZW.

Therefore, triangles are congruent by Side-Side-Angle postulate.