In the following 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 ΔABD ∼ ΔECF
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Solution
It is given that ABC is an isosceles triangle.
∴ AB = AC
⇒ ∠ABD = ∠ECF
In ΔABD and ΔECF,
∠ADB = ∠EFC (Each 90°)
∠ABD = ∠ECF (Proved above)
∴ ΔABD ∼ ΔECF (By using AA similarity criterion)
Concept: Criteria for Similarity of Triangles
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