Question

The diagonals PR and QS of a quadrilateral PQRS intersect at point O such that area of triangle OPQ is equal to area of triangle ORS. Prove that PQRS is a trapezium.​

Answer 1

PQRS is a trapezium.​  if ar (OPQ) = ar (ORS)

Step-by-step explanation:

given that:

ar Δ(OPQ) = ar Δ(ORS)

adding ar Δ(POS) on both sides

arΔ (OPQ) + ar Δ(POS) = ar Δ(ORS) + ar Δ(POS)

ar Δ(PSQ) = ar Δ(SPR)

Area of PSQ = (1/2) PS * altitude from Q at PS

Area of SPR = (1/2) PS * altitude from R at PS

=> altitude from Q at PS = altitude from R at PS

=> line joining QR ║ PS

=> PQRS is a trapezium.​

Answer 2

Hi mate

Here is your answer

Hope it will help