Question

See image below for problem, thank you :))

Answer 1

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

To prove: BX ≅ AY

Proof:

In the triangle XAM and BYM:

• ∠3 = ∠4       [vertically opposite angles]

• AM = BM     [Given]

• ∠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!