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

Checking the ratios in order to check the similarity of triangles PAB and PQR.

$\Rightarrow \dfrac{PA}{PQ} \text{ and } \dfrac{PB}{PR} \\[1em] \Rightarrow \dfrac{PA}{PQ} \text{ and } \dfrac{PB}{PB + BR} \\[1em] \Rightarrow \dfrac{5}{12.5} \text{ and } \dfrac{4}{4 + 6} \\[1em] \Rightarrow \dfrac{50}{125} \text{ and } \dfrac{4}{10} \\[1em] \Rightarrow \dfrac{2}{5} \text{ and } \dfrac{2}{5} \\[1em]$

Since, both ratios $\Big(\dfrac{PA}{PQ} = \dfrac{PB}{PR}\Big)$ are same hence by converse of basic proportionality theorem triangles are similar and so AB and QR are parallel.