Question

M and N are points on the sides PQ and PR respectively of a $\Delta PQR$. For each of the following cases, whether MN || QR:
(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm
(ii) PQ =1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

Answer 1

(1) It is given that PM = 4cm, QM = 4.5cm, PN = 4cm and NR = 4.5cm.

We have to check that $MN\parallel QR$ or not.

According to Thales theorem we have,

$\frac{PM}{QM}=\frac{PN}{NR}$

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

Hence, $MN\parallel QR$

(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$MN\parallel QR$ or not.

According to Thales theorem we have

$\frac{PM}{QM}=\frac{PN}{NR}$

Now,

$\frac{0.16}{(1.28-0.16)}=\frac{0.32}{(2.56-0.32)}$

$\frac{0.16}{\left(1.12\right)}=\frac{0.32}{\left(2.24\right)}$

$\frac{1}{7}=\frac{1}{7}$ (Proportional)

Hence, $MN\parallel QR$