In  Δ ABC, M is mid-point of AB and a straight line through M and parallel to BC cuts AC at N. If AC = 6 cm, then find the length of AN.

 

The line segment joining the mid-points of two sides of a triangle is parallel to the third side. 

The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side

Since $M$ is the midpoint of  $AB$ and  $MN\parallel BC$ hence  $N$ is the midpoint of  $AC.$Therefore

And $AN=\frac{1}{2}AC=\frac{1}{2}\times 6=3CM$