Question

Prove the midpoint theorem. In the given triangle NO || LM. KN=2.7cm, KL=5.4cm,
KO=3.9cm, Find OM. ​

Answer 1

basic proportionality theorem (NL=KL÷2=5.4÷2=2.7)

KN\NL=KO\OM

2.7/2.7=3.9\OM

OM=3.9

Answer 2

OM = 3.9 cm.

Step-by-step explanation:

We know that if a line is drawn parallel to any side of a triangle and it cuts the other two sides at two distinct points then the parallel line will cut the other two lines in the same ratio.

So, in the given triangle Δ KLM, the line NO is parallel to baseline LM, so,

$\frac{KN}{NL} = \frac{KO}{OM}$ ............ (1)

So, if the ratio is 1 : 1, then N and O will be the midpoints of sides KL and KM. (Proved)

Now, from equation (1) we get,

$\frac{2.7}{5.4 - 2.7} = \frac{3.9}{OM}$

⇒ OM = 3.9 cm. (Answer)