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Not true. They have only one base and several (3 or more) lateral triangular faces. A pyramid has a single vertex over a base - there are no parallel faces in any pyramid.
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A triangular prism has two congruent triangular bases in parallel planes and three rectangular faces joining them together. A triangular pyramid has four triangular faces, a triangular base and three triangular faces meeting at an apex above the base. Triangular prism: 6 vertices, 5 faces, 9 edges Triangular pyramid: 4 vertices, 4 faces, 6 edges
A triangular pyramid has one base, a triangle, and 3 sides, also triangles, meeting at one point, the vertex, at the top. A triangular prism has two parallel bases which are triangles, but the sides are rectangles that connect the two triangular bases.
The parallel bases would be the two triangular faces, on either end of the prism.