Question

Find the measure of KM KQ LK LR NK PM

Answer 1

Answer:

Step-by-step explanation:

Since, PN ≅ NR

RM ≅ MQ

PL ≅ LQ

QN, LR and PM are the medians and they intersect each other at point K which will be the centroid of ΔPQR.

By the property of centroid,

Point K will divide the medians in the ratio of 2 : 1

By this property,

PK : KM = 2 : 1

4 : KM = 2 : 1

$\frac{4}{KM}=\frac{2}{1}$

KM = 2

KQ = $\frac{2}{(2+1)}(NQ)$

     = $\frac{2}{3}\times 6$

KQ = 4

LK : RK = 1 : 2

LK : 3 = 1 : 2

$\frac{LK}{3}=\frac{1}{2}$

LK = 1.5

LR = LK + RK

     = 1.5 + 3

LR = 4.5

NK = $\frac{1}{(2+1)}(QN)$

     = $\frac{1}{3}(6)$

NK = 6

PM = PK + KM

PM = 4 + 2

PM = 6