Question

Prove that Triangles on the same base and between the same parallels are equal in area.

Answer 1

Given:

Triangles ABC and DBC stand on the same BC and between the same parallels l and m.

To prove:

ar(ΔABC)=ar(ΔDBC)

Construction:

CE || AB and BF || CA

Proof:

||mABCE and ||m DCBF stand on the same base BC and between the same parallels l and m.

So, ar(||mABCE)=ar (||m DCBF).......(1)

AC is a diagonal of ||m ABCE. It divides the parallelogram into two triangles of equal area.