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प्रश्न
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.
उत्तर
Given: ∆ABC in which AB = AC and AD ⊥ BC. Side CB is produced to E and EF ⊥ AC.
To prove ∆ABD ~ ∆ECF,
Proof: we know that the angles opposite to equal sides of a triangle are equal.
∠B = ∠C ...[∵ AB = AC]
Now, in ∆ABD and ∆ECF, we have
∴ ∠B = ∠C ...[proved above]
∠ADB = ∠EFC = 90°
∴ ∆ABD ~ ∆ECF ...[By AA-similarity]
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