Question

PT||QR and QT || RS. Show that ar ( PQR) = ar ( QTS )

Answer 1

triangle PQR and TQR are on the same base (QR) and between the parallels
(PT ll QR)
Therefore,
ar(PQR)=ar(TQR)                  ..... (1)
In the same way, triangle QTS and TQR are on the same base QT and between the parallels QT and RS.
So,
ar(QTS)=ar(TQR)                  ..... (2)
From (1) and (2), we have,
ar(PQR)=ar(QTS)
Hence Proved.

Answer 2

Heya !!!


Given that: PT || QR and QT || RS
To Prove: ar(ΔPQR)=ar(ΔQTS)
Proof:
Since triangle PQR and TQR are on the same base QR and between the parallels PT and QR. Therefore,
ar(ΔPQR)=ar(ΔTQR) ..... (1)
Similarly, triangle QTS and TQR are on the same base QT and between the parallels QT and RS. So,
ar(ΔQTS)=ar(ΔTQR) ..... (2)
From (1) and (2), we have,
ar(ΔPQR)=ar(ΔQTS)
Hence Proved.

Diagram is given below:-
Hope it helps u :)