Mathematics
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 △ ABD ~ △ ECF.
Triangles
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Answer
In Δ ABC,
AB = AC (Given)
∠ABC = ∠ACB (As angles opposite to equal sides are equal.) ……(1)
From figure,
∠ABD = ∠ABC and ∠ACB = ∠ECF
Substituting values of ∠ABC and ∠ACB in equation (1), we get :
⇒ ∠ABD = ∠ECF
In Δ ABD and Δ ECF,
⇒ ∠ADB = ∠EFC = 90° [∵ AD ⊥ BC and EF ⊥ AC]
⇒ ∠ABD = ∠ECF [Proved above]
∴ Δ ABD ~ Δ ECF (By A.A. axiom)
Hence, proved that Δ ABD ~ Δ ECF.
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