Geometry Glossary Essay, Research Paper
Geometry Glossary
Acute angle
- an angle whose measure is greater than 0 but less than 90 degrees; see obtuse angle
Adjacent angles
- 2 nonstraight and nonzero angles that have a common side in the interior of the angle formed by the noncommon sides
Algorithm
- a sequence of steps leading to a desired end
Alternate exterior angles
- exterior angles on alternate sides of the transversal (not on the same parallel line)
Alternate interior angles
- ditto as above, only with interior angles
Altitude
- height
Altitude of a conic solid
- the length of a segment whose endpoints are the vertex and a point on the plane of the base that is perpendicular to the plane of the base
Altitude of a cylindric solid
- the distance between the planes of the bases
Altitude of a trapezoid
- the distance between the bases of a trapeziod
Altitude of a triangle
- the perpendicular segment from a vertex to the line containing the opposite side of a triangle
Ambiguous
- not stable; changing
Analytic geometry
- see coordinate geometry
Angle
- the union of 2 rays that have the same endpoint; measured in degrees or radians (trig.); the five types of angles are zero, acute, right, obtuse, and straight
Angle bisector
- a ray that is in the interior of an angle and forms two equal angles with the sides of that angle
Angle measure between a line and a plane
- the smallest of the angles formed when a line intersects a plane
Angle side
- one of the two rays forming an angle
Antecedent
- the ‘if’ part of a conditional; represented by p; aka hypothesis, given, problem; see consequent
Area
- the amount of space taken up in a plane by a figure
Arc
- a path from one node in a network to another; doesn’t have to be straight & can be more than 1 line between 2 nodes; part of a circle; see minor arc, major arc
Arc length
- the distance between an arc’s endpoints along the path of the circle
Area(F)
- the area of figure F
Automatic drawer
- a computer program that lets you build constructions
Axis
- the line containing the vertex of a conic solid and the center of the base
Base
- the side of an isoscoles triangle whose endpoints are the vertices of the base angles
Base angle
- the angle opposite one of the equilateral sides in an isoscoles triangle
Base angle of a trapezoid
- consecutive angles that share a base of a trapezoid
Base of a conic solid
- the planar region that forms the widest point of a conic solid; often labeled as the ‘bottom’ of the conic solid, it determines the exact shape of the conic solid
Base of a cylindric solid
- the original region and its translation image
Base of a trapezoid
- the parallel sides of a trapezoid
Biconditional
- a conditional and its converse where the converse is also true; uses the words if and only if; written pq
Bilateral symmetry
- see reflection symmetry
Bisector of an angle
- see angle bisector
Bisector pf a segment
- any plane, point or two-dimensional figure containing the the midpoint of the segment and no other points on that segment
Box
- a surface made up of rectangles; a rectangular parallelpided
Capacity
- see volume
Cartesian plane
- a coordinate plane
Center of a circle
- the point that all points in the circle are equidistant from
Center of a rotation
- the point where the two intersecting lines of a rotation meet
Center of gravity
- the mean of the coordinates of points in a figure, whether one, two, or three-dimensional
Central angle of a circle
- an angle whose vertex is the center of the circle
Chord of a circle
- a segment whose endpoints are on a circle
Circle
- the set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides
Circularity
- when on a search, circling back to a previous place visited (definition, web site, etc.), usually unhelpful or redundant
Circumference
- the perimeter of a circle
Clockwise
- in orientation, the direction in which the points are named when, if traveling along the line, the interior of the polygon is on the right (got all that?); see counterclockwise
Coincidental lines
- lines that are identical (one and the same)
Colinear
- in the same line
Compass
- a drawing tool used to draw circles at different radii
Complementary angles
- 2 angles whose measures, when added together, equal 90 degrees; see supplementary angles
Composite transformation
- The composite of a first transformation S and a second transformation T is the transformation mapping a point P onto T(S(P)). When written T2 T1, do T1 first; see translation, rotation, glide reflection, similarity transformation
Concave
- see nonconvex
Concentric circles
- circles that share the same center, but have different radii
Conditional
- a statement that tells if one thing happens, another will follow; written as pq; see antecedent, consequent, converse, inverse, contrapositive
Cone
- the surface of a conic solid whose base is a circle; see right cone
Congruence tranformation
- see isometry
Congruent
- equilateral, equal, exactly the same (size, shape, etc.)
Congruent figures
- two figures where one is the image of the other under a reflection or composite of reflections; written AB
Conic section
- plane section of a cone
Conic solid
- the set of points between a point (the vertex) and a non-coplanar region (the base), including the point and the region; see cone, pyramid, regular pyramid, right cone
Conjecture
- an educated guess or opinion; a hypothesis
Consecutive sides
- sides of a polygon that share an endpoint
Consecutive vertices
- endpoints of a single side of a polygon
Consequent
- the ‘then’ part of a conditional; represented by q; aka conclusion, prove, answer
Constant of an equation
- the term that has no variable in an equation; example: C
Construction
- a precise way of drawing which allows only 2 tools: the straightedge and the compass
Contraction
- a size change where k is less than 1
Contrapositive
- a type of conditional; if not q, then not p; written q p; see inverse
Converse
- a reversed conditional; if a conditional is pq, than its converse is qp
Convex set
- a set of points in which all segments connecting points of the set lie entirely in the set; There are three things one can do to see if a figure is convex – look for “dents”, extend the segments (they shouldn’t enter the figure), and connect any two points within the figure with a segment (if any part of the segment lies outside the figure, it’s concave); see nonconvex set
Coordinate
- a number that identifies (or helps to identify) a point on a number line (or on a plane, or in space)
Coordinate geometry
- the study of geometrically representing ordered pairs of numbers
Coordinate plane
- a plane in which every point is identified with exactly 1 number and vice versa; a two-dimensional graph
Coordinatized line
- a line on which every point is identified with exactly 1 number and vice versa; a one-dimensional graph. The distance between 2 parts on a coordinatized line is the absolute value of the difference of their coordinates.
Coplanar
- within the same plane
Corollary to a theorem
- a theorem that is easily proved from the first
Corresponding angles
- any pair of angles in similar locations with respect to a transversal
Coterminal angles
- two angles that have the same terminal side
Counterclockwise
- in orientation, the direction in which points are named when, if travelling on the line, the interior of the figure is on the left side; see clockwise
Counterexample
- a situation in a conditional for which the antecedent is true, but the conditional is false; aka contradiction
Cylindric solid
- the set of points between a region and its translation in space, including the region and its image
Cylinder
- the surface of a cylindric solid whose base is a circle; see right cylinder
Cylindric surface
- the union of the bases and the lateral surface
Decagon
- a ten-sided polygon
Degree
- unit used to measure angles
Dense line
- the line that contains the shortest path between two points
Diagonal
- a segment in a polygon whose endpoints are 2 nonconsecutive vertices
Diameter of a circle (or sphere)
- the segment whose endpoints are points on a circle (or sphere) that contains the center of the circle as its midpoint; the length of that segment
Dilation
- see size change
Dilatation
- see size change
Dimensions
- the width, length, and height of a plane or space figure
Direction
- the way a number goes – positive or negative
Direction of a translation
- the compass direction in which a translation goes (duh)
Discrete Line
- a line made of dots with space inbetween their centers
Distance
- the distance between points A and B is written as AB
Distance between 2 parallel lines
- the length of a perpendicular segment between them
Dodecagon
- a twelve-sided polygon
Dot
- a description of a point in which the point has a definite size
Duodecagon
- a twelve-sided polygon
Drawing
- a freehand picture using any tool; see construction
Edge
- a segment that helps to make up a face
Empty set
- see null set
Ends of a kite
- the common vertices of the equilateral sides of a kite
Enneagon
- a nine-sided polygon
Equianglular
- having angles of the same measure
Equidistant
- the same distance from something
Equilateral
- equal in length
Equilateral triangle
- a triangle whose sides are equal in length
Even node
- a node that has an even number of arcs
Exclusive or
- one or the other, but not both
Existential statement
- a conditional that uses the word ’same’
Expansion
- a size change where k is greater than 1
Exterior angles
- angles outside of two lines cut by a transversal; see interior angles
Exterior of an angle
- the nonconvex set formed by an angle that measures less than 180 degrees; see interior of an angle
Extremes
- in the proportion , a and d; see means
Face
- a polygonal region of a surface
Family tree
- hierarchy; tower or pyramid of power or importance
Figure
- a set of points
45-45-90 triangle
- an isoscoles right triangle
Fundamental region
- a region used in a tesselation
Geometric mean
- the number g such that for two numbers a and b,
Given
- information assumed to be true in a proof
Glide reflection
- a type of composite transformation where a figure is reflected and then translated in a parallel direction
Goldback’s Conjecture
- if n is an even number greater than 2, then there are always 2 prime numbers whose sum is n
Grade
- the tilt of a real-life object in relation to the horizontal, often used to determine how steep a hill is
Graph theory
- the mathematics of complicated networks
Great circle
- the circle formed by the intersection of a sphere and the plane that contains its center and that divides the sphere into two hemispheres; see small circle
Grid
- a tesselation of congruent squares sometimes used to measure distance
Harmonic mean
- two times the product divided by the sum of the two numbers
Hemisphere
- half of a sphere
Heptagon
- a seven-sided polygon
Hexagon
- a six-sided polygon
Hidden lines
- broken lines used to signify lines that normally wouldn’t be seen in a drawing
Hierarchy
- a chart that shows varying levels of importance
Horizontal line
- a line whose slope is zero
Hypotenuse
- the side opposite the right angle in a right triangle
Icosahedron
- a 20-sided solid; each side is in the shape of a triangle
Identity reflection
- a reflection where the preimage and the image are the same; see reflection symmetry
Identitiy transformation
- a size change where k equals 1
IFF
- if and only if; see biconditional
If-then statement
- see conditional
Image
- the reflection of the preimage
Improper subset
- a subset that includes the entire parent set; see proper subset
Included angle
- the angle made by two sides of a polygon
Included side
- the side between two angles in a polygon
Inclusive or
- one or the other, or both; and/or
Infinite
- uncountable
Initial side
- the side that the measurement of an angle starts from; see terminal side
Instance of a sentence
- a situation where the statement is true
Interior angles
- angles between two lines cut by a transversal; see exterior angles
Interior of an angle
- the convex set formed by an angle that measures less than 180 degrees; see exterior of an angle
Interior of a circle
- the set of points whose distance from the center of the circle is less than that of the radius
Intersecting planes
- planes that share a line
Intersection of two sets A and B
- the set of elements which are in both A and B; written AB
Inverse
- a form of conditional; if not p, then not q; written p q
Irrational number
- decimal number that never ends, never repeats (Ex: pi)
Irregular region
- region whose boundary is not the union of circular arcs or segments
Isometry
- a transformation that keeps the same size and shape of a figure but moves it to a new location; see reflection, rotation, translation, glide reflection
Isoscoles trapezoid
- a trapezoid that has a pair of equiangular base angles
Isoscoles triangle
- a triangle with two sides of equal length
Kite
- a quadrilateral that has two distinct pairs of consecutive equilateral sides
L.A.
- lateral area
Lateral area
- the area of the lateral surface of a solid
Lateral edge
- a segment whose endpoints are corresponding points of a cylindric solid’s bases, or whose endpoints are the vertex of a conic solid and a vertex of its base
Lateral faces
- the faces of the lateral surface of a prism, or a face of a pyramid that is not a base
Lateral surface
- the surface not included in the base(s)
Lattice points
- points in the coordinate plane with integer coordinates
Leg of a right triangle
- a side of a right triangle that include the 90 degree angle
Limit
- the actual area of a region
Line
- a two-dimensional object that has no endpoints and continues on forever in a plane; formed of infinite points; the 3 orientations that lines may have are horizontal, vertical, oblique, and skew lines; written
Linear equation
- Ax + By + C = 0
Linear pair
- 2 supplementary adjacent angles whose noncommon sides form a line
Linear term of an equation
- the term with a variable, but no exponent in an equation; example: By in a linear equation
Line number
- numbers on the left side of a computer screen that tell the computer in what order to do instructions in a computer programming language such as BASIC
Line of reflection
- the line that is reflected over in a reflection
Line perpendicular to a plane
- a line perpendicular to every line in the plane that it intersects (or any one of them)
Lines of sight
- lines from an eye to what it sees that show perspective and what size to draw it
Location
- one of the four main description of a point
Locus
- the set that satisfies a given condition
Magnitude
- the value of a number; its distance from the origin
Magnitude of a rotation
- the amount of rotation in degrees
Magnitude of a translation
- the distance between any point and its image
Major arc
- an arc whose endpoints form an angle over 180 degrees with the center of the circle; written – the extra letter is used to distinguish it from a minor arc; see minor arc
Mapping
- making a transformation
Matrix
- arrangement of pixels
Mean
- average
Meaning
- a version of a conditional that defines a term, where the term is in the antecedent; see sufficient condition
Means
- in the proportion , b and c; see extremes