Question

In the given figure, if ∆ABE congruent ∆ACD, show that ∆ADE similar ∆ABC.
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Answer 1

Hence, BE = CD

And ∠DBE = ∠ECD

In Δ DBE and Δ ECD

BE = CD (proved earlier)

∠DBE = ∠ECD (proved earlier)

DE = DE (common)

Hence, Δ DBE ≅ Δ ECD

This means; DB = EC

This also means;

AD÷DB = AE÷EC

Hence; DE || BC

Thus, Δ ADE ∼ Δ ABC proved.