Given: ∠XWY ≅ ∠ZYW ∠X and ∠Z are both right angles. Prove: YXW ≅ WZY
The image is a quadrilateral WXYZ with a diagonal YW such that we get two triangles YXW and WZY. Measure of angle X and angle Z is 90 degrees. Angle XWY and angle ZYW are marked as congruent.

A. Given: ∠XWY≅∠ZYW , ∠X and ∠Z are both right angles.
∠X≅∠Z ; they have the same measure.
∠XYW≅∠ZWY ; alternate interior angles of parallel lines.
WY¯¯¯¯¯¯¯≅WY¯¯¯¯¯¯¯ ; Reflexive Property of Congruence.
YXW≅WZY by SAS
B. Given: ∠XWY≅∠ZYW , ∠X and ∠Z are both right angles.
∠X≅∠Z ; they have the same measure.
WY¯¯¯¯¯¯¯≅WY¯¯¯¯¯¯¯ ; Reflexive Property of Congruence.
YXW≅WZY by AAS
C. Given: ∠XWY≅∠ZYW , ∠X and ∠Z are both right angles.
∠X≅∠Z ; they have the same measure.
WY¯¯¯¯¯¯¯≅WY¯¯¯¯¯¯¯ ; Reflexive Property of Congruence.
YXW≅WZY by SAS