Applied Mechanics and Graphic Statics
The Law of Polygon of Forces states that

If forces acting on a point can be represented in magnitude and direction by the sides of a polygon in order, the forces are in equilibrium
If forces acting on a point can be represented in magnitude and direction by the sides of a polygon taken in order, then the resultant of the forces will be represented in magnitude and direction by t
If a polygon representing the forces acting at point in a body is closed, the forces are in equilibrium
If forces acting on a point can be represented of a polygon taken in order, their sides of a polygon taken in order, their resultant will be represented in magnitude and direction by the closing side

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Applied Mechanics and Graphic Statics
If a set of given forces are such that their free vectors build a closed polygon, then

The resultant force is zero but resultant couple may not be zero
The resultant force and resultant couple are always zero
The resultant force is zero but resultant couple is not zero
The resultant force and resultant couple both may not be zero

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