Question

In Fig., CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY).

Answer 1

According to the question,

From figure,

We get,

CD||AE

and CY || BA

To prove:

ar (ΔCBX) = ar (ΔAXY) .

Proof:

We know that,

Triangles on the same base and between the same parallels are equal in areas.

Here,

ΔABY and ΔABC both lie on the same base AB and between the same parallels CY and BA.

ar (ΔABY) = ar (ΔABC)

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

Solving and cancelling ar (ABX),

We get,

⇒ ar (AXY) = ar (CBX)