In the triangle ABC, D is the midpoint of the side BC; From the point D, the parallel straight lines of CA and BA intersect the sides BA and CA at the points E and F respectively. Let us prove that,

In Δ ABC, since D is the mid-point of BC and as FD || AB,

Then by the theorem:-

Through the mid-point of any side, if a line segment is drawn parallel to second side, then it will bisect the third side and the line segment intercepted by the two sides of the triangle is equal to half of the second side.

⇒ F is the mid-point of AC

By using the above theorem, we can also prove that E is the midpoint of AB as DE || AC.

Now as E and F have been proved to be the midpoint of AB and AC respectively, by applying the theorem:-

The line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it, we get,