Question

in the given figure AD and BE are the medians of triangle ABC and BE IS Parallel toDF .prove that CF=1/4AC

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

Answer 2

Step-by-step explanation:

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