In the given figure, MN II RP, MO II SQ, and
NP = OQ. Prove that NS = PR and OR = QS.
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Answer:
Here, using the corollary of basic proportionally theorem which states that if a line passing through the two sides of the triangle cuts it proportionally, then the line is parallel to the third side. So,
(i)
QM
PM
=
4.5
4
=
9
8
NR
PN
=
4.5
4
=
9
8
∴
QM
PM
=
NR
PN
Thus, as MN cuts the sides PQ and PR proportionally, so MN∥QR.
∴ MN∥QR
(ii)
QM
PM
=
1.28−0.16
0.16
=
1.12
0.16
=
7
1
NR
PN
=
2.56−0.32
0.32
=
2.24
0.32
=
7
1
∴
QM
PM
=
NR
PN
Thus, as MN cuts the sides PQ and PR proportionally, so MN∥QR.
∴ MN∥QR
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