Question

if m,n and r are there points on a line and n lies between m and r prove that mn +nr = mr ​

Answer 1

Answer:

Converse of basic proportionality theorem :

If a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

SOLUTION :

(i) Given : PM = 4 cm, QM = 4.5 cm, PN = 4 cm, and NR = 4.5 cm.

In ∆PQR,

PM/QM = 4/4.5

And, PN/NR = 4/4.5

so, PM/QM = PN/NR

Hence, MN || to QR

[By Converse of basic proportionality theorem]

(ii) GIVEN : PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, and PN = 0.32 cm.

MQ = PQ - PM

MQ = 1.28 - 0.16

MQ = 1.12

NR = PR - PN

NR = 2.56 - 0.32

NR = 2.24

In ∆PQR,

PM/QM = 0.16/1.12 = 1/7

And, PN/NR = 0.32/2.24 = 1/7

so, PM/QM = PN/NR

Hence, MN || to QR

[By Converse of basic proportionality theorem

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