Question

A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer.

Answer 1

Given, PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm

Then QA = QP - PA = 12.5 - 5 = 7.5 cm

Now, `(PA)/(AQ) = 5/7.5 = 50/75 = 2/3`  ......(i)

And `(PB)/(BR) = 4/6 = 2/3`  ......(ii)

From equations (i) and (ii), `(PA)/(AQ) = (PB)/(BR)`

By converse of basic proportionally theorem,

AB || QR