In the given figure, prove that ar (∆AQC) = ar (PBR)
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⏩We observe that triangles ABQ and PBQ are on the same base BQ and between the same parallels AP and BQ.
Therefore,
ar(∆ABQ)= ar(∆PBQ) .....→(i)
Similarly, triangles BCQ and BRQ are on the same base BQ and between the same parallels BQ and CR.
Therefore,
ar(∆BCQ) = ar(∆BRQ).......→ (ii)
Now,
On adding (i) and (ii), we get,
ar (∆ABQ) + ar (∆BCQ) = ar (∆PBQ) + ar(∆BRQ)
=> ar (∆AQC) = ar (∆PBR)
Hence, proved...:-)
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