10.1.1 Solid Geometry
Key Objectives • Classify three-dimensional figures according to their properties. • Use nets and cross sections to analyze three-dimensional figures. Key Terms • Each flat surface of a solid is called a face . • An edge is the segment that is the intersection of two faces. • A vertex is the point that is the intersection of three or more faces. • A prism is formed by two parallel congruent polygonal faces, called bases, connected by faces that are parallelograms. • A cylinder is formed by two parallel congruent circular bases and a curved surface that connects the bases. • A pyramid is formed by a polygonal base and triangular faces that meet at a common vertex. • A cone is formed by a circular base and a curved surface that connects the base to a vertex. • A cube is a prism with six square faces. • A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three- dimensional figure. • A cross section is the intersection of a three-dimensional figure and a plane. Example 1 Classifying Three-Dimensional Figures
Three-dimensional figures are classified and described in this example. The cone has a vertex at point A and a base that is a circle with center B . There are no edges in the cone because an edge is the intersection of two faces, or flat surfaces. There is only one face on the cone. The rectangular prism has 8 vertices and 12 edges. The rectangular prism is formed from two bases connected by faces that are parallelograms.
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