Question

Р
2.
In A PQR, PM = 15, PQ = 25
PR = 20, NR = 8. State whether line
N
M
NM is parallel to side RQ. Give
reason.
R.
0 Q
Fig. 1.36
12​

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)