Question extracted from RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions. And has been asked in several times in exams.
In this question we have question in two parts
It is given that M and N are the points on the sides PQ and PR respectively, of a ΔPQR.
Now we have to state whether MN ∥ QR.
Fow following two cases (i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm.
And second case is (ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm.
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RD sharma, DHANPAT RAI publication
(i)
Given:
In the ∆PQR
M and N are points on PQ and PR respectively
PM = 4 cm, QM = 4.5 cm, PN = 4 cm, RN = 4.5 cm
To find: MN || QR or not
According to Thales Theorem,
PM/QM = PN/NR
4/4.5 = 4/4.5
Hence, MN || QR
(ii)
Given :
Length of side PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, and PN = 0.32 cm.
To find: that MN ∥ QR or not.
MQ = PQ – PM = 1.28 – 0.16 = 1.12 cm
RN = PR – PN = 2.56 – 0.32 =2.24 cm
According to Thales Theorem,
PM/QM = PN/ RN
PM/QN = 0.16/1.12 = 1/7 – equation 1
PN/RN = 0.32/ 2.24 = 1/7 – equation 2
From equation 1 and 2
PM/QM = PN/ RN
Therefore, MN || QR