Question

The diagonals PR and QS of a quadrilateral pqrs intersect at point O such that area of triangle o p q is equal to area of triangle ORS prove that pqrs is a trapezium. pls answer and do not spam.​

Answer 1

Answer:

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

$\huge \tt{\underline{\underline{Solution}}}$

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.

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

Answer 2

Answer:

Answer:

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

$\huge \tt{\underline{\underline{Solution}}}$

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.

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$