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

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Applied Mechanics and Graphic Statics
According to Law of Triangle of Forces

If three forces acting on a, point can be represented in magnitude and direction, by the sides of a triangle taken in order, these will be in equilibrium
If the forces acting on a particle be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant will be represented in magnitude and direction by the third
Three forces acting along the sides of a triangle are always in equilibrium
Three forces acting at a point, can be rep-resented by the sides of a triangle, each side being in proportion to the force

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Applied Mechanics and Graphic Statics
Lami's theorem states that

If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
Three forces acting at a point are always in equilibrium

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