CBSE Class 10 Maths (Standard) 2024 · Paper 30(B) · Question 22(a)

Triangles 2 marks Hard

In a

△ A B C

, D and E are points on the sides AB and AC respectively such that

B D = C E

. If

∠ B = ∠ C

, then show that

D E ∥ B C

Answer

Since

∠ B = ∠ C

A B = A C

. With

B D = C E

this gives

A D = A B - B D = A C - C E = A E

, so

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

, and by the converse of the Basic Proportionality Theorem

D E ∥ B C

. Hence proved.

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