They can be any kind of triangles.
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A prism has a variety of bases but the sides are always parallelograms. A triangular prism has a triangle as the two bases and parallelograms as lateral sides. A pyramid has a variety of bases but the sides are triangles.
No, pyramids of any kind will never have any parallel faces. This is because all of the faces, excluding the base, must meet at a single point.
You would get two scalene triangles.
Right triangles - those with a 90-degree angle.
A "perpendicular bisector" is a line. There are no triangles of any kind in a line.