The Geometry of Solids

1. The Geometry of Solids Section 10.1

2. A solid formed by polygons enclosing a region is called a polyhedron. • The flat surface (or polygon) are called a face. • The segment where two faces (or polygons) meet is called an edge. • The point of intersection of three edges is called a vertex.

3. Just as we classify polygons by the number of sides, we classify polyhedron by their number of faces.

4. A regular polyhedron is a three dimensional figure where • each face of a polyhedron is a regular polygon • Each face is congruent to each other face • Each face meets other faces exactly the same way at all times

5. Prisms • A prism is a special type of polyhedron • Has two congruent bases • Bases are parallel • The other faces of the prism are called lateral faces and may be a different polygon from the base.

6. Right and Oblique Prisms • If a prism’s lateral faces are rectangles, then the prism is called a right prism. • The altitude of a prism is any perpendicular segment from one base to the other. • A prism that is not a right prism is called an oblique prism.

7. Pyramids • A pyramid is another special polyhedron. • Pyramids have just one base that is any polygon. • The other faces are called lateral faces. • The common vertex where the lateral faces meet is the vertex of the pyramid. • The altitude is a perpendicular segment from the vertex to the base.

8. Other Geometric Solids • One solid with a curved surface is a cylinder. • A cylinder, like a prism, has two congruent, parallel bases (circles). • If a segment were drawn between the centers of the two circular bases of a right cylinder it would be called an altitude. • The radius of a cylinder is a radius of the base.

9. Cones • A cone is another type of geometric solid with a curved surface. • The base is a circle. • The altitude is a perpendicular line segment from the vertex to the base.

10. Spheres • A final type of solid with curved surfaces is a sphere. • A sphere is the set of all points equidistant from a given point in space. • The radius is the given distance.

11. On an oblique cylinder the altitude would be a perpendicular line segment between the two bases.