In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason..

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In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason..

Practice Set 1.2 | Q 2 | Page 13
In ∆PQR, PM = 15, PQ = 25 PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason..

Solution

Given: PM = 15, PQ = 25, PR = 20 and NR = 8

PQ = PM + MQ
25 = 15 + MQ
⇒ MQ = 25 - 15 = 10
⇒ MQ = 10

PR = PN + NR
20 = PN + 8
⇒ PN = 20 - 8
⇒ PN = 12

`"PM"/"MQ" = 15/10 = 3/2`

`"PN"/"NR" = 12/8 = 3/2`

In ΔPQR,

`"PM"/"MQ" = "PN"/"NR"`

By converse of basic proportionality theorem, NM is parallel to side RQ or NM || RQ.

Soution:-

Given: PM = 15, PQ = 25, PR = 20, and NR = 8.

First, we find MQ and PN:

Then, we calculate the ratios of PM to MQ and PN to NR:

Since the ratios are equal, we can apply the converse of the basic proportionality theorem to conclude that NM is parallel to RQ, or NM || RQ.

Chapter 1. Similarity- Practice Set 1.2 – Page 13

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