Applied Mechanics and Graphic Statics
Varingon’s theorem of moment’s states

Algebraic sum of the moments of two forces about any point, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point
Arithmetical sum of the moments of two forces about any point, is equal to the moments of their resultant about that point
Algebraic sum of the moments of the forces about any point in their plane, is equal to the moment of their resultant about that point

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

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