Prove that ad x af=ae x ab, Mathematics

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ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB.

Ans: Consider Δ ADE and Δ ABF

∠D = ∠B = 90^o

∠E = ∠F (given)

∴Δ ADE ≅ Δ ABF

AD/AB = AE/AF

⇒ AD x AF = AB x AE Proved

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