Parallelogram ABCD

∴OB=OD,OA=OC,AB∥CD

∴∠CFO=∠AEO(∥)

Also: ∠ degree of freedom =∠BOE (equal to vertex angle)

∴△DOF≌△BOE(AAS)

∴OF=OE

OA = OC

So the quadrilateral AECF is a parallelogram (a quadrilateral with equal diagonals is a parallelogram).

Determination method of parallelogram;

1. Two groups of parallelograms with opposite sides are parallelograms.

2. Two groups of quadrilaterals with equal opposite sides are parallelograms.

3. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

4. A quadrilateral with equal diagonals is a parallelogram.