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Rajan@2021
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Asked: 2021-03-26T11:38:46+05:30 In:

In the given figure, ∠D=∠E and AD/BD=AE/EC. Prove that BAC is an isosceles triangle.

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In the given figure, ∠D=∠E and AD/BD=AE/EC. Prove that BAC is an isosceles triangle.

In the given question we have been asked to prove that BAC is an isosceles triangle. If ∠D=∠E and AD/BD=AE/EC.

ML Aggarwal Avichal Publication Class 10, similarity question no 6

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      AD/DB = AE/EC (Given)

      Therefore, DE ∥ BC (Converse of Basic Proportionality Theorem) So, ∠D = ∠B and ∠E = ∠C (Corresponding angles) (1) But ∠D = ∠E (Given)

      Therefore, ∠B = ∠C [ From (1)]

      So, AB = AC (Sides opposite to equal angles)

      i.e., BAC is an isosceles triangle

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