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B)BADADIJE FOBC) algm ABCD).13. bitthe adjointing20. In thefirec tandri |
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Answer» Constructions: DrawEOF||ABandGOH||AD.Proof:EOF||ABandDAcuts them.∴∆OABand parallelogramEABFbeing on the same base and between the same parallelsABandEF, we have:ar(∆OAB) =1/2ar(parallelogramEABF) ...(i)Similarly, ar(∆OCD) =1/2ar(parallelogramEFCD) ...(ii)On adding (i) and (ii), we get:ar(∆OAB) +ar(∆OCD) =1/2⨯ar(parallelogramEABF) +1/2ar(parallelogramEFCD)⇒ ar(∆OAB) +ar(∆OCD) =1/2⨯ ar(parallelogramABCD) (ii) ∴∆OADand parallelogramAHGDbeing on the same base and between the same parallelsADandGH, we have: ar(∆OAD) =1/2ar(parallelogramAHGD) ...(iii) Similarly, ar(∆OBC) =1/2ar(parallelogramBCGH) ...(iv)On adding (iii) and (iv), we get: ar(∆OAD) +ar(∆OBC) =1/2⨯ar(parallelogramAHGD) +1/2ar(parallelogramBCGH)⇒ ar(∆OAD) +ar(∆OBC)=1/2⨯ar(parallelogramABCD) |
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