Question

in triangle PQR,PM=15,PQ=25,PR=20,NR=8.state whether line NM is parallel to side RQ.give reason​

Answer 1

Answer:

Yep

Step-by-step explanation:

PN + NR = PR [P – N – R]  

∴ PN + 8 = 20  

∴ PN = 20 – 8 = 12  

Also, PM + MQ = PQ [P – M – Q]

∴ 15 + MQ = 25

∴ MQ = 25 - 15 = 10

PN/NR = 12/8

∴ PN/NR = 3/2   ....

(i) PM/MQ = 15/10 ∴ PM/MQ = 3/2   ...

(ii) In ∆PQR, PN/NR = PM/MQ    

...[Form (i) and (ii) ∴ line NM || side RQ [Converse of basic proportionality theorem]

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