Question

Area

12. a. The parallelograms PQRS and QRTN stand on the same base QR and between
the same parallels QR and PT, Prove that:
i. triangle PQN = triangle SRT
ii. Area of parallelogram PQRS = Area of parallelogram QRTN.​

Answer 1

Explanation:

1. In PQN & SRT.

a. <RST=<QPN (corresponding angle PQllSR)

b. <STR = <PNQ (corresponding angle TRIINQ)

c. TR=QN (Since TN & QN are opp. Side of parallelogram QNTR)

d. .°.PQN~=SRT.

2.PQN=PSOQ+SNO (whole part axiom)

3.SRT = SNO + NTRO(same as above)

4. PQN=SRT (From st. 1d)

or, PS0Q+SNO =SNO + NTRO (Cancellation of SNO)

or, PS0Q=NTRO

or, PSOQ +QOR=NTRO +QOR (Adding QOR on both side)

or, .°.◼️PQRS = ◼️QRTN

Best of luck!!!!.