Answer:
AY = BX proved.
Step-by-step explanation:
See the diagram attached to the answer.
Given AM = MB and ∠BAX = ∠ABY = 90°
Now, between ΔAXM and ΔBYM,
(i) AM = BM {Given}
(ii) ∠XAM = ∠YBM {Given}
(iii) ∠AMX = ∠BMY {Opposite angles}
So, we can say that ΔAXM ≅ ΔBYM
Hence, AX = BY.......... (1)
Now, between ΔABX and ΔABY,
(i) AB is common side.
(ii) AX = BY {Already proved} and
(iii) ∠BAX = ∠ABY {Given}
Therefore, ΔABX ≅ ΔABY.
Hence, BX = AY {Corresponding sides} (Proved)