Question

In ΔABC, if DE ∥ BC with D on AB and E on AC, prove AD/DB = AE/EC. (NCERT Class 10, Triangles – Basic Proportionality Theorem)

Answer: Since DE ∥ BC, triangles ADE and ABC are similar. Thus AD/AB = AE/AC. Rewrite as AD/(AD+DB) = AE/(AE+EC). Cross‑multiply to get AD·EC = AE·DB ⇒ AD/DB = AE/EC. Proved.

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Question

In ΔABC, if DE ∥ BC with D on AB and E on AC, prove AD/DB = AE/EC. (NCERT Class 10, Triangles – Basic Proportionality Theorem)

Answer: Since DE ∥ BC, triangles ADE and ABC are similar. Thus AD/AB = AE/AC. Rewrite as AD/(AD+DB) = AE/(AE+EC). Cross‑multiply to get AD·EC = AE·DB ⇒ AD/DB = AE/EC. Proved.