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