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