Question

In the given figure, AD and CE are medians and DF // CE.
Prove that: FB = `1/4` AB.

Answer 1

Given AD and CE are medians and DF || CE.

We know that from the midpoint theorem,
If two lines are parallel and the starting point of the segment is at the midpoint on one side, then the other point meets at the midpoint of the other side.
Consider triangle BEC. Given DF || CE and
D is the midpoint of BC.
So F must be the midpoint of BE.
So, FB = `1/2`BE but BE = `1/2`AB

Substitute value of BE in the first equation, we get
FB = `1/4`AB
Hence Proved.