# In ∆PQR, M and N are points on sides PQ and PR respectively

Question:

In ∆PQR, M and N are points on sides PQ and PR respectively such that PM = 15 cm and NR = 8 cm. If PQ = 25 cm and PR = 20 cm state whether MN || QR.

Solution:

Given $P M=15 \mathrm{~cm}, M Q=10 \mathrm{~cm}, N R=8 \mathrm{~cm}$ and $P N=12 \mathrm{~cm}$.

$\frac{P M}{P Q}=\frac{15 \mathrm{~cm}}{25 \mathrm{~cm}}=\frac{3}{5}$

$\frac{P N}{P R}=\frac{12 \mathrm{~cm}}{20 \mathrm{~cm}}=\frac{3}{5}$ $(P N=P R-N R=20-8=12 \mathrm{~cm})$

$\therefore \frac{P M}{P Q}=\frac{P N}{P R}$

So, by the converse of basic proportionality theorem MN || QR.