Chapter 12 Geometry Test

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
cross section
the of intersection of a plane and a solid
platonic solids
-tetrahedron (4 faces)
-octahedron (8 faces)
-dodecahedron (12 faces)
-icosahedron (20 faces)
Euler's Theorem
F + V = E + 2
surface area
SA= LA + 2B
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
Cavalieri's Principle
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
similar solids
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