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In figure, CD || AE and CY || BA. Prove ...

In figure, `CD || AE` and `CY || BA`. Prove that `ar (DeltaCBX) = ar (DeltaAXY)`.

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Given : `CD ||AE and CY ||BA`
To prove: `ar (Delta CBX) = ar (Delta AXY0`
Proof: Since, triangle on the same base AB and between the same parallels AB and YC are equal in area, so we have
`ar(Delta ABC) = ar(Delta ABY)`
`rArr ar(Delta CBX) + ar(DeltaABX) = ar (Delta ABX) + ar (Delta AXY)`
Hence, `ar(Delta CBX) = ar(Delta AXY)` [cancelling `ar(Delta ABX)` from both sides]
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