This paper introduces a method for recognizing geometric constraints from human demonstrations using both position and force measurements. Our key idea is that position information alone is insufficient to determine that a constraint is active and reaction forces must also be considered to correctly distinguish constraints from movements that just happen to follow a particular geometric shape. Our techniques can detect multiple plane, arc, and line constraints in a single demonstration. Our method uses the principle of virtual work to determine reaction forces from force and position data. It fits geometric constraints locally and clusters these over the whole motion for global constraint recognition. Experimental evaluations compare our force and position constraint inference technique with a similar position only technique and conclude that force measurements are essential in eliminating false positive detections of constraints in free space.