[48.4] The isosceles triangle of [48.3] must lie either on a level or on a matrix. If it lies on a level, all the straight routes of the figure must lie on rects. But on a matrix a pair of normals cannot be of the same denomination, i.e. not both rects nor both point-tracks. Thus five cases remain over for consideration. These cases are diagrammatically symbolised by the annexed figures where continuous lines represent rects, and dotted lines represent point-tracks.
Fig. 13.
Evidently case (i) is the only case in which the triangle lies on a level: the triangles in the remaining four cases lie on matrices.
The relations between the diagrams (ii) and (v) can best be seen by combining them into one figure as in (vi), and the relations between (iii) and (iv) by combining them into one figure as in (vii).
Fig. 14.
[48.5] Case (i) of [48.4] enables us to complete the congruence theory for spatial measurements. Let