Unit 10: Three-Dimensional Solids

platonic solids

a group of five special polyhedrons made of congruent regular polygonal faces with the same number of faces meeting at each vertex

diameter

a line segment that contains the center of a circle and has endpoints on the circle; this term also refers to the length of this line segment

volume

a measure of the amount of space inside a three-dimensional figure

length

a measurement taken horizontally across the longest side of an object

line segment

a part of a line with endpoints at both ends

dodecahedron

a platonic solid made from 12 congruent regular pentagons

octahedron

a platonic solid made from eight congruent equilateral triangles

tetrahedron

a platonic solid made from four congruent equilateral triangles

hexahedron

a platonic solid with six square faces

oblique pyramid

a pyramid whose vertex is not directly over the center of its regular polygon base

square

a quadrilateral with four right angles and four congruent sides and that have all the properties of parallelograms, rectangles, and rhombi

cube

a rectangular prism whose six faces are congruent squares

regular pyramid

a right pyramid whose vertex is directly over the center of a regular polygon base

polyhedron

a solid figure with no curved surfaces or edges; the faces are polygons, the edges are line segments, and the points at which the edges meet are called the vertices

perspective

a technique of representing three dimensional objects and their relationships to each other on a two dimensional surface

oblique cylinder

a three dimensional solid consisting of two parallel congruent discs not directly above each other and all the points between them

sphere

a three-dimensional figure consisting of all points in space that are the same distance from a given point

pyramid

a three-dimensional solid consisting of a base that can be any polygon, a point not in the same plane as the polygon and all the points in between them

cone

a three-dimensional solid consisting of a circular base, a vertex not on the same plane, and all the points between them

square pyramid

a three-dimensional solid consisting of a square base, a point not in the same plane as the square base, and all the points between them

cylinder

a three-dimensional solid consisting of two parallel congruent discs and all the points in between them

right cylinder

a three-dimensional solid consisting of two parallel congruent discs directly above each other and all the points in between them

oblique prism

a three-dimensional solid consisting of two parallel congruent discs not directly above each other and all the points between them

prism

a three-dimensional solid consisting of two parallel congruent polygons and all the points between them

right prism

a three-dimensional solid consisting of two parallel congruent polygons directly above each other and all the points between them

rectangular prism

a three-dimensional solid consisting of two parallel congruent rectangles and all the points between them

triangular prism

a three-dimensional solid consisting of two parallel congruent triangles and all the points between them

constant

a value in a formula that doesn't change

proportion

an equation stating that two ratios are equal; a/b = c/d if their cross products are equal: ad = bc

solid

an object that has three dimensions: length, width, and height

bases

faces of a geometric solid from which the height is drawn

similar

having exactly the same shape; corresponding angles are congruent and corresponding sides are proportional in length

one dimensional

having length but no width or height

three dimensional

having length, width, and height

zero dimensional

having no length, width, or height

axis

one of the two lines that form a Cartesian Coordinate system; horizontal is x and vertical is y

Cavalieri's Principle

prisms with different shapes as bases can also have the same volume, as long as their heights and cross-sectional areas are the same

cross-sectional area

the area of a horizontal slice of a three-dimensional solid

axis, sphere

the diameter of a sphere

slant height

the height of a two-dimensional figure that is a lateral face of a three-dimensional figure

edges

the line segments bordering each face of a solid geometric figure

width

the measurement taken from one side of an object to the other side (front to back)

height, basic

the measurement taken from the bottom to the top of an object

point

the most basic object in geometry, used to mark and represent locations. They have no length, width, or height

height

the perpendicular distance between the base of a geometric figure and the opposite vertex or parallel base

lateral faces

the plane figures that make up the surfaces of a solid geometric figure that are not bases of the figure

base area

the sum of the areas of all base surfaces in a three-dimensional figure, it is added to the lateral area of the figure to get the surface area

lateral area

the sum of the areas of all nonbase surfaces in a three-dimensional figure; this + base area = surface area

Pythagorean Theorem

the theorem that relates the side lengths of a right triangle; a^2 + b^2 = c^2

surface area

the total area of the exterior surface of a solid figure

icosahedron

a 20-sided solid in which each side is a polygon, regular ones have equilateral triangle faces

right cone

a cone whose vertex is directly over the center of its circular base

oblique cone

a cone whose vertex is not directly over the center of its circular base

Cartesian coordinate system

a coordinate system formed by two number lines, one horizontal and one vertical intersecting at the zero point of each line called axes