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.

Answer 1

Given PM = 15 cm,MQ = 10 cm , NR = 8 cm  and  PN = 12 cm .

 

\[\frac{PM}{PQ} = \frac{15cm}{25cm} = \frac{3}{5}\]
\[\frac{PN}{PR} = \frac{12cm}{20cm} = \frac{3}{5} \left( PN = PR - NR = 20 - 8 = 12cm \right)\]
\[ \therefore \frac{PM}{PQ} = \frac{PN}{PR}\]

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