In triangle ABC, M is the midpoint of AB and a straight line through M and parallel to BC cuts AC in N. Find the length of AN and MN, if BC = 7 cm and AC = 5 cm.

According to the converse of the midpoint theorem,

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 || BC. 

Hence, N is the midpoint of AC and $\mathrm{MN}=\frac{1}{2}\mathrm{BC}$.

So,

$\mathrm{AN}=\frac{1}{2}\mathrm{AC}$

$\mathrm{AN}=\frac{1}{2}\left(5\right)=2.5 \mathrm{cm}$

and also  $\mathrm{MN}=\frac{1}{2}\mathrm{BC}$

$\mathrm{MN}=\frac{1}{2}\times 7=3.5 \mathrm{cm}$

Therefore, the length of AN and MN are 2.5 cm and 3.5 cm respectively.