Question

AD and BE are medians of triangle ABC and DF parallel BE.Prove that CF =1fourth AC?

Answer 1

E is the midpoint of AC
therefore
EC = 1/2 AC

D is the midpoint of BC
And BE || DF
therefore
F is the midpoint of EC
[converse midpoint theorem]

CF = 1/2 x EC
= 1/2 x (1/2 x AC )
=1/4 x AC