Question

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.

(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 , , and .

We have to check that or not.

According to Thales theorem we have

(Proportional)

Hence,

(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 or not.

According to Thales theorem we have

Now,

$$\begin{gathered} \frac{PM}{MQ}=\frac{0.16}{1.12}=\frac{1}{7} \\ \frac{PN}{NR}=\frac{0.32}{2.24}=\frac{1}{7} \\ \therefore \frac{0.16}{1.12}=\frac{0.32}{2.24} \end{gathered}$$

Hence,