If in a parallelogram ABCD, E and F are points on the diagonal AC such that $$\overline{AE} = \overline{FC}$$ than quadrilateral BEDF is a:​

Correct option is D

Given: 

If  parallelogram ABCD,

E and F  points on the diagonal AC 

$$\overline{AE} = \overline {FC}$$   

Solution:  

​Parallelogram Diagonal Bisector Property:

The diagonals of a parallelogram bisect each other, meaning that the point where the diagonals intersect divides them into two equal parts.

Therefore, if E and F lie on diagonal AC,

AE = FC 

In $$\triangle ADE$$ and $$\triangle CBF$$ 

From congruency we get:

ED = BF 

Similarly, in $$\triangle ABE$$ and $$\triangle CDF$$ 

BE = DF 

Also, diagonal BD > diagonal EF 

So, BEDF is a parallelogram