Question

In the below fig. X and Y are the mid-points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that ar (∆ ABP) = ar (∆ACQ).

Answer 1

Since x and y are the midpoint AC and AB respectively

XY || BC

Clearly, triangles BYC and BXC are on the same base BC and between the same parallels XY and BC

We observe that the quadrilateral XYAP and XYAQ are on the same base XY and between the same parallel XY and PQ.