Geometry - Unit 8 - Solid Geometry

LESSON 2 ORTHOGRAPHIC, ISOMETRIC, AND PERSPECTIVE DRAWINGS---------------------------------------------------------------

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right cone

a cone in which the axis of the cone is perpendicular to the base

axis of a cone

a segment that extends from the apex of a cone to the center of the base

LESSON 2 THREE-DIMENSIONAL FIGURES----------------------------

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LESSON 3 FORMULAS FOR THREE-DIMENSIONAL FIGURES---------

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LESSON 4 PROPERTIES OF PRISMS-------------------------------------

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LESSON 5 PROPERTIES OF CYLINDERS--------------------------------

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LESSON 6 PROPERTIES OF PYRAMIDS---------------------------------

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LESSON 7 PROPERTIES OF CONES-------------------------------------

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LESSON 8 PROPERTIES OF SPHERES-----------------------------------

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great circle

a circle formed by the intersection of the surface of a sphere with a plane that passes through the center of the sphere

oblique cone

a cone in which the axis of the cone is not perpendicular to the base

oblique cylinder

a cylinder in which its axis is not perpendicular to its bases

right cylinder

a cylinder in which its axis is perpendicular to its bases

base of a geometric solid

a face of a three-dimensional figure by which the figure is measured or classified

perspective drawing

a form of three-dimensional projection in which all nonvertical parallel lines appear to meet at a distant point, called the vanishing point

isometric projection

a form of three-dimensional projection in which all three planes are drawn parallel to established axes and at full scale

Orthographic Projection

a form of three-dimensional projection that presents six views of an object in which the line of sight for each view is perpendicular to the plane of the figure

cone

a geometric solid formed by a circular base and a curved surface that connects the base to a vertex

pyramid

a geometric solid formed by a polygonal base and triangular lateral faces that meet at a common vertex

cylinder

a geometric solid formed by two congruent, circular bases and a curved surface that connects the bases

prism

a geometric solid formed by two parallel, congruent bases connected by faces that are parallelograms

polyhedron

a geometric solid in which four or more polygons intersect only at their edges; plural is polyhedra

non-polyhedron

a geometric solid that contains at least one curved surface

horizon

a horizontal line on a perspective drawing that contains the vanishing point(s)

vanishing point

a point on the horizon where nonvertical parallel lines appear to meet in a perspective drawing

projected point

a point that lies on one of the three planes of a three-dimensional coordinate system and corresponds to two of the numbers in an ordered triple

oblique prism

a prism in which at least one of the lateral faces is not a rectangle

right prism

a prism in which each lateral face is a rectangle

right pyramid

a pyramid in which the altitude of the pyramid extends from the apex to the center of the base

oblique pyramid

a pyramid in which the altitude of the pyramid extends from the apex to the plane of the base not at the center of the base

irregular pyramid

a pyramid whose base is not a regular polygon

cube

a rectangular prism with six square faces

regular pyramid

a right pyramid whose base is a regular polygon

radius of a sphere

a segment that connects the center of the sphere with any point on the surface of the sphere

axis of a cylinder

a segment that extends from one base of a cylinder to the other base and whose endpoints are the centers of the two bases

altitude of a cone

a segment that extends from the apex of a cone to the plane of its base and is perpendicular to the plane of the base

altitude of a pyramid

a segment that extends from the apex of a pyramid to the plane of its base and is perpendicular to the plane of the base

ordered triple

a set of three numbers that indicates the position of a point in space on a three-dimensional coordinate system

isometric dot paper

a sheet of paper with rows of dots that are arranged so they are oriented 30° from the horizontal

geometric solid

a three-dimensional figure that encloses a region of space

net

a two-dimensional diagram of the surfaces of a three-dimensional figure that can be folded to form a geometric solid

three-dimensional projection

a two-dimensional representation of a three-dimensional figure drawn on a given plane as it would be seen from a particular direction or according to a particular set of rules

linear perspective

a visual phenomenon in which the apparent size of objects with respect to their distance from the viewer are determined by means of intersecting lines that radiate from a point on the horizon

lateral face

any face of a prism that is not a base

face of a geometric solid

each flat surface of a three-dimensional figure

hemisphere

half of a sphere

Cavalieri's principle

if two geometric solids with the same height have the same cross-sectional area at every level, then they have the same volume

lateral surface of a cone

the curved surface that connects the base of a cone to the apex of the cone

lateral surface of a cylinder

the curved surface that connects the two bases of a cylinder

slant height of a cone

the distance from the apex of a right cone to a point on the edge of the base

slant height of a pyramid

the distance from the apex to the midpoint of an edge where a lateral face meets the base

cross section of a geometric solid

the intersection of a geometric solid with a plane

sphere

the locus of points in space that are a fixed distance from a point called the center of the sphere

volume of a geometric solid

the number of non overlapping unit cubes of a given size that will fill the interior of a geometric solid

vertex of a geometric solid

the point that is the intersection of three or more faces of a three-dimensional figure

edge of a geometric solid

the segment that is formed by the intersection of two faces of a three-dimensional figure

lateral area

the sum of the areas of all of the lateral surfaces of a geometric solid

surface area

the total area of all the faces and curved surfaces of a geometric solid

apex of a cone

the vertex of a cone

apex of a pyramid

the vertex opposite the base where all the lateral faces meet