Given: ∠XWY ≅ ∠ZYW, ∠X and ∠Z are both right angles. Prove: YXW ≅ WZY
The image is of a regular rectangle YZWX, alternate interior angles formed by its diagonal YW are marked as equal.

A. It is given that ∠XWY≅∠ZYW, and ∠X and ∠Z are both right angles. So ∠X≅∠Z by the Transitive Property of Congruence. WY≅YW and ZW≅ZY by the Reflexive Property of Congruence. So △YXW≅△WZY by ASA.
B. It is given that ∠XWY≅∠ZYW, and ∠X and ∠Z are both right angles. So ∠X≅∠Z because all right angles are congruent. WY≅YW by the Reflexive Property of Congruence. So △YXW≅△WZY by AAS.
C. It is given that ∠XWY≅∠ZYW, and ∠X and ∠Z are both right angles. So ∠X≅∠Z by the Transitive Property of Congruence. WY≅YW by the Reflexive Property of Congruence. So △YXW≅△WZY by ASA.
D. It is given that ∠XWY≅∠ZYW, and ∠X and ∠Z are both right angles. So ∠X≅∠Z because all right angles are congruent. WY≅YW by the Reflexive Property of Congruence. So △YXW≅△WZY by ASA.