A rectangular pyramid has a rectangular base and four triangular faces that meet at a single point (the apex). In the net of a rectangular pyramid, the rectangular base counts as one face, and the four triangular faces differ based on the dimensions of the base.
- The rectangular base is one set of congruent faces.
- The four triangular faces can be divided into two sets of congruent faces if the base has equal adjacent side lengths (special case). Otherwise, if the base is a rectangle (non-square), the triangular faces will generally not be congruent, leading to:
Overall, regardless of whether the triangular faces are congruent or not, the rectangular base is a unique set of congruent faces.
Thus, in the typical case of a rectangular pyramid with an unequal rectangle, there is 1 set of congruent faces (the rectangular base).
Therefore, the total number of sets of congruent faces in the net of a rectangular pyramid is 1.