We will study solids. A solid is a 3-dimensional closed shape. There are many types…some have flat faces and others have curves faces. We will study a little of both types.
The ones with flat faces are polyhedra. Polyhedra have faces that are all polygons. If the faces are all regular polygons, then they are regular polyhedra. Some polyhedra may have different, non-regular polygons (like a polyhedron made up of acute triangles and rectangles).
We will study the following polyhedra (plural): prisms and pyramids.
We will study the following solids (that are not polyhedra): cylinders, cones, spheres.
A prism is a polyhedron with 2 parallel and congruent bases. There are right prisms and oblique prisms. Right prisms have lateral edges that are perpendicular to the bases (so they are the altitudes of the prism), while oblique prisms are slanted. The lateral faces of a right prism are always congruent rectangles. The lateral faces of an oblique prism are always congruent parallelograms.
A cylinder also has 2 congruent and parallel bases but they are circles. Therefore a cylinder is NOT a polyhedron. It has a curved surface area.
A pyramid has only one base that can be any polygon (regular or not). If it is a right pyramid, then its lateral faces are always congruent isosceles triangles. If the pyramid is oblique, then the lateral faces are simply triangles.
A cone is like the pyramid in that it also has one base, but it is a circle. Therefore a cone is NOT a polyhedron (since it has a curved surface area).
A sphere is the set of all points in space equidistant from a given point, called the center. It is NOT a polyhedron.
We will learn about Platonic solids later.
A plane may slice any solid and we will be interested in the shape of the cross-section. It can be hard to visualize when all you have is the picture of the solid.
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