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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.
Solution
Given PM = 15 cm,MQ = 10 cm , NR = 8 cm and PN = 12 cm .
\[\frac{PN}{PR} = \frac{12cm}{20cm} = \frac{3}{5} \left( PN = PR - NR = 20 - 8 = 12cm \right)\]
\[ \therefore \frac{PM}{PQ} = \frac{PN}{PR}\]
So, by the converse of basic proportionality theorem MN || QR.
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