# geometry chapter 12

## 36 terms

### polyhedron

a solid that is bounded by polygons, called faces, that encloses a single region of space

### edge

a line segment formed by the intersection of two faces of a polyhedron

### vertex

a point where three of more edges of polyhedron meet

### regular polyhedron

a convex polyhedron in which all of the faces are congruent regular polygons

### convex polyhedron

any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron. if this segment goes outside the polyhedron, then the polyhedron is non convex or concave

### platonic solids

five regular polyhedra named after plato

### tetrahedron

a polyhedron with four faces

### cube

a polyhedron with six congruent square faces

### octahedron

a polyhedron with eight faces

### dodecahedron

a polyhedron with twelve faces

### icosahedron

a polyhedron with twenty faces

### cross section

the intersection of a plane and a solid

### prism

a polyhedron with two congruent faces, called bases, that lie in parallel planes

### lateral faces

the faces of a prism that are parallelograms formed by connecting the corresponding vertices of the bases of the prism

### lateral edges

the segments connecting the corresponding vertices of the bases of a prism

### surface area

the sum of the areas of the faces of a polyhedron or other solid

### lateral area

the sum of the areas of the lateral faces of a polyhedron or other solid with one or two bases

### net

the two dimensional representation of the faces of a polygon

### right prism

a prism in which each lateral edge is perpendicular to both bases

### oblique prism

a prism with lateral edges that are not perpendicular to the bases

### cylinder

a solid with congruent circular bases that lie in parallel planes

### right cylinder

a cylinder in which the segment joining the centers of the bases is perpendicular to the bases

### pyramid

a polyhedron in which the base is a polygon, and the lateral faces are triangles with a common vertex, called the vertex of the pyramid

### regular pyramid

a pyramid that has a regular pyramid for a base and in which the segment joining the vertex and he center of the base is perpendicular to the base

### slant height

the slant height is the distance between the vertex and a point on the base edge

### cone

a solid that has one circular base and a vertex that is not in the same plane as the base

### right cone

a cone in which the segment joining the vertex and the enter of the base is perpendicular to the base.

### lateral surface

consists of all segments that connect the vertex with the points on the edge of the base

### volume

the number of cubic units contained in the interior of a solid

### sphere

the set of all points in space equidistant from a given point called the center of the sphere

a segment from the center of a sphere to a point on the sphere. the distance from the center of a sphere to any point on the sphere

### chord

a segment whose endpoints are on a sphere

### diameter

a chord that contains the center of a sphere. The distance across a sphere through its center

### great circle

the intersection of a sphere and a plane that contains the center of the sphere

### hemisphere

half of a sphere, formed when a great circle separates a sphere into two congruent halves

### similar solids

two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii