Question

Question 11 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

Class 10 - Math - Triangles Page 141

Answer 1

Sol:-

sense ,∆ABC s

AB = AC

∆ABD and ∆ECF s

<ABD = <ECF

<ADB = <EFC = 90°

.°. ∆ABD ~ ∆ECF ( criteria of AA )

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Answer 2

It is given that ABC is an isosceles triangle.
∴ AB = AC
⇒ ∠ABD = ∠ECF
In ΔABD and ΔECF,
∠ADB = ∠EFC (Each 90°)
∠BAD = ∠CEF (Proved above)
∴ ΔABD ~ ΔECF (By using AA similarity criterion)