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.

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.

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