AMSCO'S Geometry. New York - Rye High School

Chapter Summary 465• Perpendicular planes are two planes that intersect to form a right dihedralangle.• A line is perpendicular to a plane if and only if it is perpendicular to eachline in the plane through the intersection of the line and the plane.• A plane is perpendicular to a line if the line is perpendicular to the plane.• Parallel planes are planes that have no points in common.• A line is parallel to a plane if it has no points in common with the plane.• The distance between two planes is the length of the line segment perpendicularto both planes with an endpoint on each plane.• A polyhedron is a three-dimensional figure formed by the union of thesurfaces enclosed by plane figures.• The portions of the planes enclosed by a plane figure are called the facesof the polyhedron.• The intersections of the faces are the edges of the polyhedron, and theintersections of the edges are the vertices of the polyhedron.• A prism is a polyhedron in which two of the faces, called the bases of theprism, are congruent polygons in parallel planes.• The sides of a prism that are not bases are called the lateral sides.• The union of two lateral sides is a lateral edge.• If the line segments joining the corresponding vertices of the bases of aprism are perpendicular to the planes of the bases, then the prism is a rightprism.• The altitude of a prism is a line segment perpendicular to each of thebases with an endpoint on each base.• The height of a prism is the length of an altitude.• A parallelepiped is a prism that has parallelograms as bases.• A rectangular parallelepiped is a parallelepiped that has rectangular basesand lateral edges perpendicular to the bases.• The lateral area of the prism is the sum of the areas of the lateral faces.• The total surface area of a solid figure is the sum of the lateral area andthe areas of the bases.• A pyramid is a solid figure with a base that is a polygon and lateral facesthat are triangles.• A regular pyramid is a pyramid whose base is a regular polygon andwhose altitude is perpendicular to the base at its center.• The length of the altitude of a triangular lateral face of a regular pyramidis the slant height of the pyramid.• A cylinder is a solid figure formed by congruent parallel curves and thesurface that joins them.