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 $\parallel$ QR.

Answer 1

We have, $PM=15cm,NR=8cm,PQ=25cm$ and $PR=20cm$

Now,

$MQ=PQ-PM=25-15=10cm$ and $PN=PR-NR=20-8=12cm$

Hence,

$\frac{PM}{MQ}=\frac{15}{10}=\frac{3}{2}$

Also,

$\frac{PN}{NR}=\frac{12}{8}=\frac{3}{2}$

$\therefore$ $MN\parallel QR$ [ By converse proportionality theorem ]