Question

In the figure ,PT||QR and QT||RS.show that ar(∆PQR=ar(∆QTS

Answer 1

see the attachment given :-

solution:-

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.