Exercise 120 Page 137

Let's first prove that △ XYW ≅ △ ZWY. We already know that the triangles have one pair of congruent angles. Examining the diagram, we can also see a pair of alternate interior angles, ∠ ZWY and ∠ XYW. Since WZ ∥ YX, we can say that they are congruent according to the Alternate Interior Angles Theorem.

Since the triangles have two pairs of congruent angles, the triangles are similar by the AA (Angle-Angle) Similarity Theorem. Next, notice that WY is a side that is shared by the triangles. Therefore, we know that this side is congruent by the Reflexive Property of Congruence.

Now we can claim congruence between the triangles by the AAS (Angle-Angle-Side) Congruence Theorem. Let's show this as a flowchart.