Q) In the figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that Δ ABD ~ Δ ECF.

Ans:

Since Δ ABC is an isosceles triangle, hence AB = AC

∴ ∠ B = ∠ C ……….. (i)

Next, we compare Δ ABD and Δ ECF

∠ ADB = ∠ EFC   (given as 90⁰)

∠ B = ∠ C             (by equation i)

Therefore by AA identity, Δ ABD $\sim$ Δ ECF

Hence Proved !

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