Points K, M and N are the midpoints of sides AB, BC and AC of triangle ABC.

Points K, M and N are the midpoints of sides AB, BC and AC of triangle ABC. Prove that the example of triangle KMN is equal to half the perimeter of triangle ABC.

Considering that points K, M and N are the midpoints of the sides AB, BC, AC, respectively, then KM is the middle line in the triangle ABC.

Also MN and KN are also midlines in triangle ABC.

Any midline in a triangle is parallel to the side it does not touch and is equal to half of that side.

So: KM = AC: 2; MN = AB: 2; KN = BC: 2.

We find the perimeter of the triangle ABC:

P (ABC) = AB + BC + AC.

Perimeter of triangle KMN:

P (KMN) = KM + MN + KN = AC: 2 + AB: 2 + BC: 2 = (AB + BC + AC): 2 = P (ABC): 2.

That is, the perimeter of triangle KMN is equal to half of the perimeter of triangle ABC.