Question

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

Answer 1

Solution-

By 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,

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

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

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

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

$\Rightarrow \frac{3}{5}=\frac{3}{5}$

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

Therefore, NM || RQ.(Proved)

Answer 2

Answer

PQ=PM+MQ.............. (P-M-Q)

25=15+MQ

MQ=25-15

MQ=10

PR=PN+NR.........…....(P-N-R)

20=PN+8

PN=20-8

PN=12

NOW PM = 15=3........... (1)

MQ =10=2

AND PN=12=3.................(2)

NR=8=2

IN TRAINGLE POR PM =PN..(FROM 1,2)

MQ=NR

SEG NM 11 SIDE OR.... (BPT)