In the figure (2) given below, DE || BC. Prove that
(i) area of ∆ACD area of ∆ABE (ii) area of ∆OBD = area of ∆OCE
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BC∣∣DE
△DEC and △DEB lies on the same base and between the same parallel lines
So ar(△DEC)=ar(△DEB)
(1) on adding ar(△ADE) in both sides of equation (1) we get
ar(△DEC)+ar(△ADE)=ar(△ADE)+ar(△ADE)
ar(△ACD)=ar(△ABE)
(2) on substracting ar(ODE) from both sides of equation (1) we get
ar(△DEC)−ar(△ODE)=ar(△DEB)−ar(△ODE)
⇒ ar(△OCE)=ar(OBD)
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