In ∆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 || QR.

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Solution

Given and .
$\frac{P M}{P Q} = \frac{15 cm}{25 cm} = \frac{3}{5} \frac{P N}{P R} = \frac{12 cm}{20 cm} = \frac{3}{5} (P N = P R - N R = 20 - 8 = 12 cm) ∴ \frac{P M}{P Q} = \frac{P N}{P R}$

So, by the converse of basic proportionality theorem MN || QR.

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Similar questions

Q. In

△

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

∥

QR.

Q. M and N are points on the sides PQ and PR respectively of a ∆PQR. For each of the following cases, state whether MN || QR.

(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm
(ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

M and N are points on the sides PQ and PR respectively of a $Δ P Q R$ . For each of the following cases, whether MN || QR:
(i) PM = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm
(ii) PQ =1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

Q. M and N are points on the sides PQ and PR respectively of a

△

PQR. For each of the following cases, state whether MN

∥

QR :

(i) PM = 4 cm,QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm

(ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm

Q. M and N are points on the sides PQ and PR respectively of a

Δ P Q R

. For each of the following cases state whether MN is parallel to QR
A. PM= 4, QM = 4.5, PN = 4, NR = 4.5
B. PQ= 1.28, PR= 2.56, PM = 0.16, PN= 0.32

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In ∆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 || QR.

Given and . PMPQ=15cm25cm=35PNPR=12cm20cm=35 PN=PR-NR=20-8=12cm∴PMPQ=PNPR So, by the converse of basic proportionality theorem MN || QR.

Given and .
$\frac{P M}{P Q} = \frac{15 cm}{25 cm} = \frac{3}{5} \frac{P N}{P R} = \frac{12 cm}{20 cm} = \frac{3}{5} (P N = P R - N R = 20 - 8 = 12 cm) ∴ \frac{P M}{P Q} = \frac{P N}{P R}$

So, by the converse of basic proportionality theorem MN || QR.