Question

In the following figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that ∆ABC ≅ ∆DEF.

Answer 1

Given: In the following figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC.

To show: ∆ABC ≅ ∆DEF

Proof: Since, BF = EC

On adding CF both sides, we get

BF + CF = EC + CF

⇒ BC = EF   ...(i)

In ∆ABC and ∆DEF,

∠A = ∠D = 90°  ...[∵ BA ⊥ AC and DE ⊥ DF]

BC = EF   ...[From equation (i)]

And BA = DE   ...[Given]

∴ ∆ABC ≅ ∆DEF   ...[By RHS congruence rule]