Question

if D is midpoint of side BC of triangle ABC, P and Q are points lying respectively on side AB and AC such that DP is parallel to QA. Prove that area of Traingle CPQ is equal to 1/4th area of traingle ABC

Answer 1

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Answer 2

Midpoint of Δ ABC = D (Given)

Point  on side AB = P (Given)

Point on side AC = Q (Given)

DP║QA (Given)

Area of ΔPDQ = Area of ΔPDA (As triangles are on the same base and  between the same parallels PD & AQ)

Area of  ΔBQP) = Area of ΔPBD) + Area of ΔPDQ

= Area of ΔBQP = Area of ΔPBD + Area of Δ PDA

Thus,

Area of ΔBQP = Area of Δ BDA

Since AD is the median , dividing ΔABC into two triangles with equal area, thus -

= Area of ΔBQP = 1/2 Area of ΔABC