Question

E is the mid-point of side AB and F is the mid-point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram.

Answer 1

Let us draw a parallelogram ABCD Where F is the midpoint Of side DC and E is the mid-point of side AB of a parallelogram  ABCD.

To prove:  AEFD is a parallelogram

Proof: 
In parallelogram ABCD
AB || DC
BC || AD
AB = DC
`1 /2"AB" = 1/2`DC
AE = DF
Also AD || EF
Therefore, AEFD is a parallelogram.