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Question
In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.
Solution
Given: PM = 15, PQ = 25, PR = 20 and NR = 8
PQ = PM + MQ
25 = 15 + MQ
⇒ MQ = 25 - 15 = 10
⇒ MQ = 10
PR = PN + NR
20 = PN + 8
⇒ PN = 20 - 8
⇒ PN = 12
`"PM"/"MQ" = 15/10 = 3/2`
`"PN"/"NR" = 12/8 = 3/2`
In ΔPQR,
`"PM"/"MQ" = "PN"/"NR"`
By converse of basic proportionality theorem, NM is parallel to side RQ or NM || RQ.
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