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Mathematics

Basic Proportionality Theorem

PM =4 cm; QM ...

Question

PM =4 cm; QM =4.5 cm;
PN = 4 cm; NR = 4.5 cm

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Solution

$\frac{P M}{Q M} = \frac{4}{4.5}$ and $\frac{P N}{N R} = \frac{4}{4.5}$
$∴ \frac{P M}{Q M} = \frac{P N}{N R}$ $[E a c h r a t i o = \frac{4}{4.5}]$
$\Rightarrow$ By the converse of Basic Proportinality theorem, we get, MN $∥$ QR.

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Similar questions

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 ∆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

Construct the following quadrilaterals.

(i) Quadrilateral $A B C D$

$A B = 4.5 c m$

$B C = 5.5 c m$

$C D = 4 c m$

$A D = 6 c m$

$A C = 7 c m$

(ii) Quadrilateral

J U M P

J U = 3.5 c m

U M = 4 c m

M P = 5 c m

P J = 4.5 c m

P U = 6.5 c m

(iii) Parallelogram

M O R E

O R = 6 c m

R E = 4.5 c m

E O = 7.5 c m

(iv) Rhombus

B E S T

B E = 4.5 c m

E T = 6 c m

Q. Construct a quadrilateral

L I F T

, when:

L I = 4 c m, I F = 3 c m, T L = 2.5 c m, L F = 4.5 c m, I T = 4 c m

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PM =4 cm; QM =4.5 cm;PN = 4 cm; NR = 4.5 cm

PMQM=44.5 and PNNR=44.5 ∴PMQM=PNNR [Eachratio=44.5] ⇒ By the converse of Basic Proportinality theorem, we get, MN ∥ QR.

PM =4 cm; QM =4.5 cm;
PN = 4 cm; NR = 4.5 cm

$\frac{P M}{Q M} = \frac{4}{4.5}$ and $\frac{P N}{N R} = \frac{4}{4.5}$
$∴ \frac{P M}{Q M} = \frac{P N}{N R}$ $[E a c h r a t i o = \frac{4}{4.5}]$
$\Rightarrow$ By the converse of Basic Proportinality theorem, we get, MN $∥$ QR.