a solid that is bounded by polygons, called faces, that enclose a single region of space
an edge of a polyhedron is a line segment formed by the intersection of two faces
a vertex of a polyhedron is a point where three or more edges meet
if a polyhedron is regular if all of its faces are congruent regular polygons
a polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron
the of intersection of a plane and a solid
-tetrahedron (4 faces)
-octahedron (8 faces)
-dodecahedron (12 faces)
-icosahedron (20 faces)
F + V = E + 2
Volume Congruence Postulate
if two polyhedra are congruent, then they have the same volume
Volume Addition Postulate
the volume of a solid is the sum of the volumes of all its non-overlapping parts
if two solids have the same height and the same cross-sectional area at every level, then they have the same volume
volume of a prism or cylinder
volume of a pyramid or cone
the locus of points in space that are a given distance from a point (center of the sphere)
radius of a sphere
a segment from the center to a point on the sphere
chord of a sphere
a segment whose endpoints are on the sphere
two solids with equal ratios of corresponding linear measures, such as heights or radii
Similar Solids Theorem
if two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a^2:b^2, and corresponding volumes have a ratio of a^3:b^3
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