The faces of a regular triangular pyramid are:
Congruent
Similar
In a regular triangular pyramid, all of its faces are triangles.
(The base is an equilateral triangle and the lateral faces are triangles in a pyramid)
All the edges are equal in length.
Hence the triangles formed by all the faces are congruent triangles.
All congruent triangles are similar.
Therefore, the faces of a regular triangular pyramid are congruent and similar.