Consider first the resultant of two non-collinear forces P and Q. We know that when lines representing P and Q are drawn to scale, one after the other, the line joining the starting point to the end point represents the resultant in magnitude and direction; the actual position of the resultant however is through the point of intersection of P and Q.

 

 

 

 

 

 

Now if a force R is added to P and Q so that the three forces are in equilibrium, R must cancel out the effect of the resultant of P and Q. Hence R is equal and opposite to this resultant and passes through the point of intersection of P and Q.

 

 

 

 

 

 

 

 

Therefore

             

three forces in equilibrium must be concurrent and

can be represented in magnitude and direction

by the sides of a triangle taken in order.

This triangle is known as a triangle of forces and it can be used to solve a problem if, in the diagram, there

already is a triangle whose sides are parallel to the forces acting. Such a triangle is similar to the triangle of

forces so the lengths of its sides are proportional to the magnitudes of the corresponding forces.