Question

M and N are points on the sides PQ and PR respectively of a ΔPQR. For each of the following cases, state whether MN II QR.

(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm 

(ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

Answer 1

(i) we have PM=4cm, QM=4.5 cm,PN=4 cm and NR=4.5 cm 

Hence PM/QM=4/4.5=40/45=8/9 

PN/NR=4/4.5=40/45=8/9 

PM/QM= PN/NR 

by the converse of proportionality theorem 

MN∥QR 

(ii) we have PQ=1.28cm, PR=2.56 cm,PM=0.16 cm and PN=0.32 cm

Hence PQ/PR=1.28/2.56=128/256=1/2

PM/PN=0.16/0.32=16/32=1/2

PQ/PR = PM/PN

by the converse of proportionality theorem

MN∥QR