Question

Pt parallel Qr and QT PARALLEL RS. SHOW THAT ar (∆PQR)=at (∆QTS).

Answer 1

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.