Adv
deepaksoni
  • 0
Guru

M and N are the points on the sides PQ and PR respectively, of a ΔPQR. For each of the following cases, state whether MN ∥ 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.

  • 0

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.

 

learning CBSE maths in effective way.
RD sharma, DHANPAT RAI publication

Share

1 Answer

  1. (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

    • 0
Leave an answer

Leave an answer

Browse

Choose from here the video type.

Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions