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Similarities:

Both are based on one shape.Both are regular polyhedra.Both have a cross section which resembles the base shape.Both can be set at an "oblique" angle (where the top of the shape is not at 90° with the base).

Differences:

Pyramids: Have a similar cross-section. Prisms have a congruent cross section.Similar means roughly similar to. The proportions of the object or shape stay the same, (such as the angle size), but the side length and position do not.

Pyramids have x number of triangular faces that meet at the apex, where x is the number of sides the base polygon has.

Prisms have x number of rectangular faces that meet at an identical base polygon shape, where x is the number of sides the base polygon has.

A Prism doesn't have to be pyramid shaped, since the name refers to a device which splits light and not the shape of the object.

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Q: How are prisms and pyramids the same how are they different?
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