Given: ∠XAM = ∠YBM = 90° and AM = BM
To prove: BX ≅ AY
Proof:
In the triangle XAM and BYM:
- ∠3 = ∠4 [vertically opposite angles]
- ∠XAM = ∠YBM [Both are 90°]
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:
- ∠1 = ∠2 [vertically opposite angles]
- AM = BM [Given]
- XM = MY [Proved above]
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!
