Question

In the figure AB=CF, EF=BD and ∠AFE=∠CBD. Prove that (i) Δ AFE ≅ Δ CBD, (ii) ∠D=∠E.

Answer 1

i) We have,
AB=CF
=> AB+BF=CF+BF
=> AF=CB - - - - (i)

In triangles AFE and CBD, we have
AF=CB [From (i)]
∠AFE = ∠DBC [Given]
EF=BD [Given]

So, by SAS criterion of congruence, we have
Δ AFE ≅ Δ CBD

ii) Since, Δ AFE ≅ Δ CBD
therefore, ∠D=∠E [C. P. C. T.]

Answer 2

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