ABCD is a parallelogram

`therefore" "AB=DCand AB"||"DC`

`implies" "2AE=2CFand AE"||"CF`

`implies" "AE=CFand AE"||"CF`

`impliessquareAECF` is a parallelogram

`therefore" "AF"||"EC`

In `DeltaDCM,`

F is the mid-point of DC

and `FN"||"CM`

`therefore` N is the mid-point of DM.

`implies" "DN=MN" "...(1)`

In `DeltaBAN,`

E is the mid-point of AB.

`and" "EM"||"AN`

`therefore` M is the mid-point of BN.

`implies" "BM=MN" "...(2)`

From eqs, (1) and (2)

`" "BM=MN=ND`

`implies` AF and CE, divides the diagonal BD into three equal parts.