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

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