Question

In the adjoining figure,
PM = 4.8, MR = 2.4, P-
ON = 5.4, NR = 3.6.
State with reason
whether seg MN is
parallel to side PQ or
not?
​

Answer 1

Answer:

ratio PM/MR=4.8/2.4=2:1

ratio ON/NR=5.4/3.6=3:1

Since the two ratios are not equal, therefore

MN is not parallel to PQ

Answer 2

Given :   PM = 4.8, MR = 2.4, P-

ON = 5.4, NR = 3.6.

To Find : seg MN is parallel to side PQ  or not

Solution:

Thales theorem / BPT ( Basic Proportionality theorem )

if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

Converse :

if a line intersecting the  two sides,   in the same ratio then it is parallel to 3rd side.

PM = 4.8  ,

MR = 2.4

=> PM/MR = 4.8/2.4 = 2/1

QN = 5.4

NR = 3.6

=> QN/NR  = 5.4/3.6  = 3/2

2/1  ≠ 3/2

PM/MR ≠  QN/NR  

Hence MN is not parallel to PQ

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