Q) In a Δ ABC, D and E are points on the sides AB and AC respectively such that BD = CE. If ∠B = ∠C, then show that DE ǁ BC

Ans: Let’s start with the diagram for he given question:

Step 1: We are given ∠ B = ∠ C,

∴ AB = AC  (being the sides opposite to equal angles)

∴ (AD + DB) = (AE + CE)

We are given that BD = CE,

∴ (AD + BD) = (AE + BD)

∴ AD = AE

Step  2: Next, in ABC, now we have AD = AE and BD = CE

∴

Now, by converse of Basic Proportionality Theorem,

DE ǁ BC

Hence Proved !

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