Q) In the given figure, Δ ABE ≅ Δ ACD. Prove that Δ ADE ~ Δ ABC.

(Q 22- 30/3/3 – CBSE 2026 Question Paper)

Ans:

Step 1: Given that Δ ABE ≅ Δ ACD

∴ By CPCT, AB = AC

and AD = AE

and CD = BE

Step 2: Let’s calculate ratio of AD and AB,

Since, AB = AC, and AD = AE

∴

∵ Converse of BPT theorem state that “if a line intersects two sides of a triangle and divides them in the same ratio, then the line is parallel to the third side of the triangle”

∴ DE is parallel to BC

Step 3: By comparing Δ ADE and Δ ABC

∠ ADE = ∠ ABC (∵ DE ǁ BC)

∠ A = ∠ A (∵ Common angle)

∴ by AA similarity criterion,

Δ ADE ~ Δ ABC

Hence Proved!

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