CBSE Class 10 Maths (Standard) 2025 · Paper 30(B)/S · Question 21(b)

Triangles 2 marks Medium

If a line intersects sides

A B

and

A C

△ A B C

D

and

E

respectively, and is parallel to

B C

, prove that

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

Answer

\frac{A D}{A B} = \frac{ar ( △ A D E )}{ar ( △ A B E )} = \frac{ar ( △ A D E )}{ar ( △ A D C )} = \frac{A E}{A C}

, because

ar (△ A B E) = ar (△ A D C)

when

D E ∥ B C

. Hence proved.

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