Question

AD and BE are medians of ,Δ and BE||DF. Prove that CF = ¼ 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