Question

In the given figure, AP is parallel to BC, BP is parallel to CQ.
Prove that the area of triangles ABC and BQP are equal.

Answer 1

Joining PC we get,

ΔABC and ΔBPC are on the same base BC and between the same parallel lines AP and BC.
∴ A( ΔABC ) = A( ΔBPC )          ....(i)

ΔBPC and ΔBQP are on the same base BP and between the same parallel lines BP and CQ.
∴ A( ΔBPC ) = A( ΔBQP )          ....(ii)

From (i) and (ii), we get
∴A( ΔABC ) = A( ΔBQP ) 
Hence proved.