Chapter 10 Vocabulary - Discovering Geometry

polyhedron

• A solid whose surface consists of polygons and their interiors, each of which is a face.
• The surface area, SA, of a sphere with radius r is given by the formula SA = 4πr^2.
• A polyhedron with a polygon base and line segments connecting the vertices of the base with a single point (the vertex of the pyramid) that is not coplanar with the base.
• (of a cylinder) The line segment connecting the centers of the bases. (Lesson 10.1)

face of a polyhedron

• A line segment drawn from the vertex of a figure perpendicular to its base or the line containing the base, or the length of the altitude segment. See cone, cylinder, parallelogram, prism, pyramid. (Lessons 3.3, 8.1, 10.1)
• (of a polyhedron) One of the polygons and its interior forming the surface of a polyhedron. (Lesson 10.1)
• The volume of a prism or a cylinder is the area of the base (B) multiplied by the height (H) of the solid.
• (of a circle or sphere) The point from which all points on the figure are the same distance. (circle: Lessons 1.6, 6.1, 6.4; sphere: Lesson 10.1)

edge

• (of a solid) The intersection of two faces. (Lesson 10.1)
• The surface area, SA, of a sphere with radius r is given by the formula SA = 4πr^2.
• (of a polyhedron) One of the polygons and its interior forming the surface of a polyhedron. (Lesson 10.1)
• A polyhedron with two congruent polygons in parallel planes as bases. Line segments (lateral edges) connect the corresponding bases to form lateral faces, which are parallelograms.

vertex

• The intersection of a sphere with a plane that passes through its center. (Lesson 10.1)
• The surface area, SA, of a sphere with radius r is given by the formula SA = 4πr^2.
• A point of intersection of two or more rays or line segments in a geometric figure. See angle, polygon, and polyhedron. (Lessons 1.1, 1.4, 10.1)
• If B is the area of the base of a pyramid or cone and H is the height of the solid, then the formula for volume is V = 1/3BH.

tetrahedron

• (of a prism or pyramid) A face other than a base. (Lesson 10.1)
• A polyhedron with four faces. The regular tetrahedron is one of the Platonic solids. (Lesson 10.1)
• A solid whose surface consists of a circle and its interior, and all points on line segments that connect points on the circle to a single point (the cone's vertex) that is not coplanar with the circle.
• The set of all points in space at a given distance (the radius) from a given point (the center). (Lessons 1.8, 10.1)

prism

• If B is the area of the base of a pyramid or cone and H is the height of the solid, then the formula for volume is V = 1/3BH.
• A solid whose surface consists of polygons and their interiors, each of which is a face.
• A polyhedron with two congruent polygons in parallel planes as bases. Line segments (lateral edges) connect the corresponding bases to form lateral faces, which are parallelograms.
• A side of a polygon or face of a solid used for reference when drawing an altitude or other feature. See cone, cylinder, isosceles triangle, parallelogram, prism, pyramid, trapezoid. (Lessons 1.5, 5.3, 10.1)

bases

• A side of a polygon or face of a solid used for reference when drawing an altitude or other feature. See cone, cylinder, isosceles triangle, parallelogram, prism, pyramid, trapezoid. (Lessons 1.5, 5.3, 10.1)
• A solid whose surface consists of a circle and its interior, and all points on line segments that connect points on the circle to a single point (the cone's vertex) that is not coplanar with the circle.
• (of a prism or pyramid) A face other than a base. (Lesson 10.1)
• A polyhedron with a polygon base and line segments connecting the vertices of the base with a single point (the vertex of the pyramid) that is not coplanar with the base.

lateral faces

• The surface area, SA, of a sphere with radius r is given by the formula SA = 4πr^2.
• (of a prism or pyramid) A face other than a base. (Lesson 10.1)
• The volume of a sphere with radius r is given by the formula V = 4/3πr^3.
• (of a prism or pyramid) The intersection of two lateral faces. (Lesson 10.1)

lateral edges

• (of a prism or pyramid) The intersection of two lateral faces. (Lesson 10.1)
• A polyhedron with two congruent polygons in parallel planes as bases. Line segments (lateral edges) connect the corresponding bases to form lateral faces, which are parallelograms.
• The set of all points in space at a given distance (the radius) from a given point (the center). (Lessons 1.8, 10.1)
• A solid whose surface consists of polygons and their interiors, each of which is a face.

altitude of a prism or height

• A polyhedron with two congruent polygons in parallel planes as bases. Line segments (lateral edges) connect the corresponding bases to form lateral faces, which are parallelograms.
• A line segment drawn from the vertex of a figure perpendicular to its base or the line containing the base, or the length of the altitude segment. See cone, cylinder, parallelogram, prism, pyramid. (Lessons 3.3, 8.1, 10.1)
• A measure of the amount of space contained in a solid. (Lesson 10.2)
• The set of all points in space at a given distance (the radius) from a given point (the center). (Lessons 1.8, 10.1)