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Draw lines XY and WZ through P such that XY⊥AB and WZ⊥BC, with X on AB, Y on CD, W on AD, Z on BC. Th en XY⊥CD and WZ⊥ AD ∵AB||CD and AD||BC. Now area ABCD = AB.XY = AB.(PX + PY) AB.PX + BC.PY (∵AB = BC). Similarly area ABCD = AD.PW + BC.PZ. So AB.PX + BC.PY = AD.PW + BC.PZ →ΔAPB + ΔCPD = ΔADP + ΔBPC.
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