See image below for problem, thank you :))

Given: ∠XAM = ∠YBM = 90°    and     AM = BM

To prove: BX ≅ AY

Proof:

In the triangle XAM and BYM:

From the ASA rule of congruency, we can say that: ΔXAM ≅ ΔYBM

Since ΔXAM ≅ ΔYBM: We can say that XM ≅ MY     [CPCT - Common Part of Congruent triangles]

In the Triangle AMY and XMB:

From the SAS rule of congruency, we can say that: ΔAMY ≅ ΔXMB

Since ΔAMY ≅ ΔXMB: We can finally say that BX ≅ AY    [CPCT]

Hence Proved!