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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» (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 |
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