Q9 of 186 Page 184

ΔABC and ΔDBC lie on the same side of BC, as shown in the figure. From a point, P on BC, PQ || AB and PR || BD are drawn, meeting AC at Q and CD at R respectively. Prove that QR || AD.

We can observe two triangles in the figure.

In ∆ABC,


PQ ∥ AB


Applying Thale’s theorem, we get


…(i)


In ∆BDC,


PR ∥ BP


Applying Thale’s theorem, we get


…(ii)


Comparing equations (i) and (ii),



Now, applying converse of Thale’s theorem, we get


QR ∥ AD


Hence, QR is parallel to the AD.


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