Question

D and E are points on the sides AB and AC respectively of a ∆ABC such that DE।।BC and divides ∆ABC into two equal parts, equal in area.Find BD/AB.

Answer 1

We have
area (Δ ADE) = area (trapezium BCED)
⇒ area (Δ ADE) + area (Δ ADE)
= area (trapezium BCED) + area (Δ ADE)
⇒ 2 area (Δ ADE) = area (Δ ABC)   ...(i)
In Δ ADE and Δ ABC, we have
∠ADE = ∠B,      ...[∵ DE | | BC]
∴ ∠AED = ∠C   ...(corresponding angles)]
and ∠A = ∠A,    ...[Common]