Q) In the given figure, DE ∥ AC and DF ∥ AE. Prove that : BF/FE = BE/EC.

(Q 22 – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s compare Δ ABE and Δ DBF

Here, ∠ BDF = ∠ BAE

(∵ DF ǁ AE)

∠ B = ∠ B (common angle)

By AA Similarity criterion, Δ ABE ~ Δ DBF

∴

∴

∴

∴ ………….. (i)

Step 2: Let’s compare Δ ABC and Δ DBE

Here, ∠ BDE = ∠ BAC

(∵ DE ǁ AC)

∠ B = ∠ B (common angle)

By AA Similarity criterion,

Δ ABC ~ Δ DBE

∴

∴

∴

∴ ………. (ii)

Step 3: By comparing equations (i) and (ii), we get:

∴

by inversing both sides, we get:

∴  

Hence proved !

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