between the plates A, B and C to exist, the following condition must be satisfied: AvB + BvC + CvA = 0 where AvB is the relative motion of B with respect to A. This condition can be represented in velocity space by constructing a velocity triangle ABC where the lengths AB, BC and CA are proportional to the velocities AvB, BvC and CvA respectively. Further conditions must also be met for the triple junction to exist stably – the plates must move in a way that leaves their individual geometries unchanged. Alternatively the triple junction must move in such a way that it remains on all three of the plate boundaries involved. McKenzie and Morgandemonstrated that these criteria can be represented on the same velocity space diagrams in the following way. The lines ab, bc and ca join points in velocity space which will leave the geometry of AB, BC and CA unchanged. These lines are the same as those that join points in velocity space at which an observer could move at the given velocity and still remain on the plate boundary. When these are drawn onto the diagram containing the velocity triangle these lines must be able to meet at a single point, for the triple junction to exist stably. These lines necessarily are parallel to the plate boundaries as to remain on the plate boundaries the observer must either move along the plate boundary or remain stationary on it. For a ridge the line constructed must be the perpendicular bisector of the relative motion vector as to remain in the middle of the ridge an observer would have to move at half the relative speeds of the plates either side but could also move in a perpendicular direction along the plate boundary. For a transform fault the line must be parallel to the relative motion vector as all of the motion is parallel to the boundary direction and so the line ab must lie along AB for a transform fault separating the plates A and B. For an observer to remain on a trench boundary they must walk along the strike of the trench but remaining on the overriding plate. Therefore, the line constructed will lie parallel to the plate boundary but passing through the point in velocity space occupied by the overriding plate. The point at which these lines meet, J, gives the overall motion