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