It is a rectangle which is similar to the base.
A prism can have a triangular cross-section with a rectangular base
Pyramid, triangular prism, cone.
It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.
A triangular prism has a triangular cross-section. A rectangular prism has a rectangular cross-section.
triangle
It is a rectangle which is similar to the base.
a square
A triangular prism has a uniformed cross-section whereas a rectangular pyramid does not.
A prism can have a triangular cross-section with a rectangular base
a square
Pyramid, triangular prism, cone.
a triangular pyramid
A solid with a triangular cross section when the cross section is taken parallel to the base could be either a triangular prism, a triangular pyramid, or a triangular frustrum.. I've been sitting here trying to convince myself (without actually bearing down and trying to prove it mathematically) that any cross section of a regular tetrahedron (a special case of triangular pyramid) taken perpendicularly to the base is a triangle, and I THINK this is the case, but as I said I certainly haven't rigorously proven it; I'm just unable to come up with any obvious situation where this is not true.
It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.
cone, cylinder, rectangular prism, square pyramid and triangular prism
A triangular prism has a triangular cross-section. A rectangular prism has a rectangular cross-section.