The first thing we notice is that the triangles share a side, WY. By the Reflexive Property of Congruence, we can say that this sides are congruent to itself.
If we view WY as a transversal to XY and WZ, we can show that ∠1 and ∠3 are congruent by the Alternate Interior Angles Theorem. This is possible because XY and WZ are parallel.
Using the same theorem, we can show that ∠2 and ∠4 are congruent if we instead let WY be a transversal to WX and YZ,
Let's summarize what we have found in a final diagram.
Since two angles and the included side from one triangle are congruent with two angles and the included side in the other triangle, we can claim congruence by the ASA Congruence Theorem.
