In the following figure, CD || AE and CY || BA. Prove that ar (∆CBX)

1.	In the following figure, CD \|\| AE and CY \|\| BA. Prove that ar (∆CBX) = ar (∆AXY).
Answer» Given: CD \|\| AE and CY \|\| BE To prove: ar (∆CBX) = ar (∆AXY) Proof: Since, ∆ABC and ∆BAY both lie on the same base AB and between the same parallel AB and CY. ar (∆ABC) = (∆BAY) ⇒ ar (∆ABX) + ar (∆CBX) = ar (∆ABX) + ar (∆AXY) ⇒ ar (∆CBX) = ar (∆AXY) [Eliminating ar (∆ABX) from both sides] Hence proved.

In the following figure, CD || AE and CY || BA. Prove that ar (∆CBX) = ar (∆AXY).

Answer»

Given: CD || AE and CY || BE

To prove: ar (∆CBX) = ar (∆AXY)

Proof: Since, ∆ABC and ∆BAY both lie on the same base AB and between the same parallel AB and CY.

ar (∆ABC) = (∆BAY)

⇒ ar (∆ABX) + ar (∆CBX) = ar (∆ABX) + ar (∆AXY)

⇒ ar (∆CBX) = ar (∆AXY)

[Eliminating ar (∆ABX) from both sides]

Hence proved.