The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F , where E is any point on the…

CBSE Class 10 Maths PYQ · Triangles · Similarity with Triangles · 5 Marks · March 2025 · Standard

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1155 Marks · March 2025 · Standard

The diagonal $BD$ of a parallelogram $ABCD$ intersects the line segment $AE$ at the point $F$, where $E$ is any point on the side $BC$. Prove that $DF \times EF = FB \times FA$.

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Correct figure. In $\Delta ADF$ and $\Delta EBF, \angle DFA = \angle EFB, \angle ADF = \angle FBE. \therefore \Delta ADF \sim \Delta EBF \implies \frac{DF}{FB} = \frac{FA}{EF} \implies DF \times EF = FB \times FA$.