CBSE Class 10 Maths (Basic) 2025 · Paper 430/4/1 · Question 25

Triangles 2 marks Medium

In the given figure

∠ A D E = ∠ A C B

and

\frac{A D}{D B} = \frac{A E}{E C}

. Prove that

△ A B C

is an isosceles triangle.

Triangle with line DE inside

Answer

Since

\frac{A D}{D B} = \frac{A E}{E C}

D E ∥ B C

, so

∠ A B C = ∠ A D E = ∠ A C B

. The sides opposite these equal angles give

A B = A C

, so

△ A B C

is isosceles. Hence proved.

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