Question

In $\triangle PQR$, M and N are points on sides PQ and PR respectively such that PM = 15 cm and NR = 8 cm. If PQ = 25 cm and PR = 20 cm state whether $MN \parallel QR$.

Answer 1

Given:  

In ΔPQR,  M and N are points on sides PQ and PR.

PM = 15 cm, NR = 8 cm

PQ = 25 cm, PR = 20 cm

In ΔPQR,  

PM/PQ = 15 /25 = ⅗

PM/PQ = 3/5

and

PN/PR = (PR – NR)/PR

PN/PR = (20 - 8)/20

PN/PR = 12/20 = ⅗

PN/PR = ⅗  

So, PM/PQ = PN/PR

Hence, MN || QR

[By the converse of basic proportionality theorem]

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

$\huge\mathcal{SOLUTION}$

Given :

In $\triangle PQR$, M and N are points on sides PQ and PR respectively .

And .....

● PM = 15 cm

● NR = 8 cm

● PQ = 25 cm

● PR = 20 cm

● $MN \parallel QR.$ =??

Solve :

In $\triangle PQR$ ,

$\frac{PM}{PQ} = \frac{15}{25}$

$\frac{PM}{PQ} = \frac{3}{5 }$ .....(i)

And ,

$\frac{PN}{PR}$

= $\frac{PR - NR}{PR}$

= $\frac{20 - 8}{20}$

= $\frac{12}{20}$

= $\frac{3}{5}$ .....(ii)

From eq (i) and (ii) ....

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

● $MN \parallel QR.$ ..(by converse of basic proportionality theorem ).

Hence , $MN \parallel QR.$.