Applied Mechanics and Graphic Statics
A point subjected to a number of forces will be in equilibrium, if

Algebraic sum of the forces is zero
Algebraic sum of the moments of the forces about the point is zero
Sum of resolved parts in any two directions at right angles, are both zero
Two resolved parts in any two directions at right angles are equal

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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 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 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 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
Parallelogram Law of Forces states, "if two forces acting simultaneously on a particle be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by

The diagonal of the parallelogram which passes through the point of intersection of the forces
Its longer side
The diagonal of the parallelogram which does not pass through the point of intersection of the forces
Its shorter side

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