CBSE Class 10 Maths (Standard) 2025 · Paper 30/1/1 · Question 33(a)

Triangles 5 marks Medium

The diagonal

B D

of a parallelogram

A B C D

intersects the line segment

A E

at the point

F

, where

E

is any point on the side

B C

. Prove that

D F \times E F = F B \times F A

Answer

Since

△ A D F \sim △ E B F

(AA similarity),

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

, and cross-multiplying gives

D F \times E F = F B \times F A

. Hence proved.

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