M and N are points on the sides PQ and PR respectively of a ∆PQR. For each of the following cases, state whether MN || QR.

(1)lt is given that $P M=4 \mathrm{~cm}, Q M=4.5 \mathrm{~cm}, P N=4 \mathrm{~cm}$ and $N R=4.5 \mathrm{~cm}$.

We have to check that $M N \| O R$ or not.

According to Thales theorem we have

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

$\Rightarrow \frac{4}{4.5}=\frac{4}{4.5}$ (Proportional)

Hence, $M N \| Q R$

(2) It is given that PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm and PN = 0.32 cm.

We have to check that $M N \| Q R$ or not.

According to Thales theorem we have

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

Now,

$P M M Q=0.161 .12=17 P N N R=0.322 .24=17 \therefore 0.161 .12=0.322 .24$

Hence, $M N \| Q R$