Math, asked by rohitchoudhari12121, 9 months ago

In triangle PQR, PM=15,PQ=25 PR=20,NR=8. state whether line NM be is parallel to side RQ ,Give reason​

Answers

Answered by pavan2005rajak
1

Answer:

your answer is here

Step-by-step explanation:

applying contradiction, we can prove that NM is parallel to RQ.

Let's assume, NM || RQ

Then,

ΔPRQ ≈ ΔPNM, as

∠P is common to both the triangles

∠PNM = ∠PRQ (as corresponding angle of parallel lines)

∠PMN= ∠PQR (as corresponding angle of parallel lines)

Applying similar triangle properties,

\Rightarrow \frac{PN}{PR}=\frac{PM}{PQ}⇒

PR

PN

=

PQ

PM

\Rightarrow \frac{PR-NR}{PR}=\frac{PM}{PQ}⇒

PR

PR−NR

=

PQ

PM

\Rightarrow \frac{20-8}{20}=\frac{15}{25}⇒

20

20−8

=

25

15

\Rightarrow \frac{12}{20}=\frac{15}{25}⇒

20

12

=

25

15

\Rightarrow \frac{3}{5}=\frac{3}{5}⇒

5

3

=

5

3

As the ratios came out to be same, so what we had assumed was correct.

Therefore, NM || RQ.(Proved)

Answered by BlackWizard
5

Answer:

Given:

PM = 15,

PQ = 25,

PR = 20 and NR = 8

Now, PN = PR − NR

= 20 − 8

= 12

Also, MQ = PQ − PM

= 25 − 15

= 10

In △PRQ, PR/NR=12/8

=3/2

Also,PM/MQ=15/10

=3/2

∴PR/NR=PM/MQ

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

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