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, ${\displaystyle \frac{\text{PA}}{\text{AQ}}}$

= ${\displaystyle \frac{5}{7.5}}$

= ${\displaystyle \frac{50}{75}}$

= ${\displaystyle \frac{2}{3}}$  ...(i)

And ${\displaystyle \frac{\text{PB}}{\text{BR}}}$

= ${\displaystyle \frac{4}{6}}$

= ${\displaystyle \frac{2}{3}}$  ...(ii)

From equations (i) and (ii),

${\displaystyle \frac{\text{PA}}{\text{AQ}}=\frac{\text{PB}}{\text{BR}}}$

By converse of basic proportionally theorem,

AB || QR