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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 In figure, `" " CD || AE`
and `" " CY || BA`
To prove `" " ar (DeltaCBX) = ar (DeltaAXY)`
Proof We know that, triangles on the same base and between the same parallels are equal in areas.
Here, `DeltaABY` and `DeltaABC` both lie on the same base AB and between the same parallels CY and BA.
`therefore" "` `ar (DeltaABY) = ar (DeltaABC)`
`rArr" "` `ar (ABX) + ar (AXY) = ar (ABX) + ar (CBX)`
`rArr" "` `ar (AXY) = ar (CBX)" "` [eliminating ar (ABX) from both sides]
`" "` Hence proved.
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