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 twodimensional 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 threedimensional
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 noncoplanar 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 twodimensional graph
Coordinatized line
 a line on which every point is identified with exactly 1 number and vice versa; a onedimensional 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 tensided 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 twelvesided polygon
Dot
 a description of a point in which the point has a definite size
Duodecagon
 a twelvesided 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 ninesided 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
454590 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 reallife 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 sevensided polygon
Hexagon
 a sixsided 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 20sided 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
Ifthen 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 twodimensional 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
Measure
 the amount of openness in an angle
Measure of an arc
 The measure of minor arc or major arc is the measure of its central angle.
Median
 the segment connecting the vertex of an angle in a triangle to the midpoint of the side opposite it
Midpoint
 the point M of where AM = AB
Minor arc
 an arc whose endpoints form an angle less than 180 degrees with the center of the circle; written ; see major arc
Net
 a 2D figure that can be folded on its segments or curved on its boundaries to form a 3D figure; see article here
Network
 a group of nodes and arcs
Ngon
 a polygon with n sides
Node
 a description of a point in a network where it is possible for two different segments to share the same endpoints
Nonagon
 a ninesided polygon
Nonconvex set
 a set of points in which not all segments connecting points of the set lie entirely in the set; synonym: concave; see convex set
NonEuclidean geometry
 solid geometry
Nonincluded side
 the side of a triangle that is not included by 2 given angles
Nonoverlapping regions
 regions that don’t share interior points
Nonperspective drawing
 a threedimensional drawing that doesn’t use perspective
Null set
 a set with nothing in it
Number line
 a coordinatized line
Oblique prism or cylinder
 a nonright prism or cylinder
Oblique line
 a line that has a definite slope not equal to zero
Obtuse angle
 an angle whose measure is greater than 90 but less than 180 degrees; see acute angle
Octagon
 an eightsided polygon
Odd node
 a node with an odd number of arcs
Onedimensional
 having length, but no width; examples: a line, a ray, a segment
Opposite faces
 faces that lie in parallel planes
Opposite rays
 two rays with a common endpoint that form a line
Ordered pair
 the two numbers that (called coordinates) are used to identify a point in a plane; written (x, y)
Ordered triple
 the three numbers (called coordinates) that are used to identify a point in space; written (x, y, z)
Orientation
 in an image change, the direction in which the points named go (i.e., how A’s position relates to B’s and B’s relates to C’s); either clockwise or counterclockwise for figures
Overlapping triangles
 triangles that share a side or angle
Parallel lines
 two or more coplanar lines that have no points in common or are identical (eg, the same line)
Parallelogram
 a quadrilateral with both pairs of opposite sides parallel
Parallelpiped
 a prism whose opposite faces are all parallelograms and congruent (in pairs)
Parallel planes
 planes that have no points in common
Pentadecagon
 a 15sided polygon
Pentagon
 a fivesided polygon
Perimeter of a polygon
 the sum of the lengths of the sides of the polygon
Perpendicular bisector
 the bisector of a segment perpendicular to it
Perpendicular lines
 2 segments, rays, or lines that form a 90 degree angle
Perpendicular planes
 planes in which any two intersecting lines, one in each plane, form a right angle
Perspective
 feeling of depth
Perspective drawing
 a drawing in which, in order to show perspective, oblique parallel lines will meet
Pi
 written p ( for those of you who can’t read math tags yet); the ratio C/D where C is the circumference and D is the diameter of a circle; 3.14159265359
Pixel
 small dot of color that makes up computer and TV screens
Plane
 a twodimensional group of points that goes on infinitely in all directions; made up of infinite lines
Plane figure
 a set of points that are on a plane
Plane geometry
 the study of twodimensional figures in a plane
Plane section
 the intersection of a figure with a plane
Point
 a zerodimensional figure; while usually left undefined, has four main representions – the dot, the node, the location, and the ordered pair of numbers
Polarity of a variable
 the positivity or negativity of a variable; its direction
Polygon
 a union of 3 or more segments where each segment intersects 2 other segments, one at each endpoint; “many sided”; see reflex polygon
Polygonal region
 the union of a polygon and its interior
Polyhedron
 a threedimensional surface which is the union of polygonal regions and has no holes
Postulate
 a statement assumed to be true without proof; see theorem
Preimage
 the original object that is reflected
Prism
 the surface of a cylindric solid whose base is a polygon; see right prism, parallelpiped, box
Proof
 a sequence of justified conclusions used to prove the validity of an ifthen statement
Proper subset
 a subset that doesn’t include everything in its parent set; see improper subset
Proportion
 a statement that two ratios are equal
Proportional
 one of four numbers that form a true proportion
Protracter
 a tool used to measure angles
Prove
 the goal of a proof
Pyramid
 the surface of a conic solid whose base is a polygon; see regular pyramid
Pythagorean triple
 a set of three numbers that can be side lengths of a right triangle
Q.E.D.
 “quod erat demonstrandum” (Latin) This stems from medieval translators’ habitual tendency of translating the Greek for “this was to be demonstrated” to the Latin phrase above. This appeared originally at the end of many of Euclid’s propositions, signifying that he had proved what he set out to prove.
Q.E.F.
 “quod erat faciendum” is the latin for “which was to be done” It appears in Latin translations of Euclid’s works signifying that he had demonstrated what he had set out to demonstrated.
Quadrangle
 a foursided polygon; see quadrilateral
Quadratic equation
 Ax2 + By + C = 0
Quadratic term of an equation
 the term Ax2 in a quadratic equation
Quadrilateral
 a foursided polygon; see rhombus, parallelogram, square, rectangle, trapezoid, isoscoles trapezoid, kite
R
 rotation
r
 radius
Radii
 plural form of radius
Radius
 the segment whose endpoints are any point on a circle or sphere and its center; the length of that segment
Rate
 a ratio where the quantities are of different kinds; example: 60 miles per hour
Ratio
 a quotient of 2 numbers
Ratio of similtude
 the ratio of the length of an image to the length of the preimage
Ray
 a onedimensional figure that consists of one endpoint A, one point B, all of the points on , and all points for which B is between them and A; written
Rectangle
 a quadrilateral whose angles are all right angles
Rectangular solid
 the union of a box and its interior
Reference angle
 the angle of less than 360 degrees that corresponds to an angle of over 360 degrees; In order to get the reference angle, you must subtract 360 degrees from the given angle until there is less than 360 degrees left.
Refine
 to change a conjecture slightly so that it is true
Reflecting line
 see line of reflection
Reflection image
 For a point A not on the reflecting line, its reflection image is the point B where the reflecting line is the perpendicular bisector of . For a point A on the reflecting line, its reflection image is itself.
Reflection image of a figure
 the set of all of the reflection images of points in the figure
Reflection notation
 rm(ABC), which stands for the reflection over line m of figure ABC
Reflectionsymmetric figure
 a figure that shows reflection symmetry
Reflection symmetry
 a characteristic of a figure in which there is a reflection line where its reflection is itself
Reflex polygon
 a polygon for which 2 or more of its sides intersect each other
Region
 the union of a figure and its interior
Regular polygon
 a convex polygon whose angles and sides are all congruent
Regular pyramid
 a pyramid whose base is a regular polygon and whose vertex forms a segment with the center of the polygon perpendicular to its plane
Resolution
 the density of pixels in a picture
Rhombus
 a parallelogram with four equilateral sides
Right angle
 an angle whose measure is 90 degrees
Right cone
 a cone whose axis is perpendicular to the plane containing its base
Right cylinder
 a cylinder whose direction of sliding is perpendicular to the plane of the base
Right prism
 a prism whose direction of sliding is perpendicular to the plane of the base
Right triangle
 a triangle that has a 90 degree angle
Rotation
 the composite of two reflections over intersecting lines
S.A.
 surface area
Scale factor
 size change magnitude
Scalene triangle
 a triangle with no equilateral sides
Secant to a circle
 a line that intersects the circle in two points
Sector
 part of a circle containing its center and an arc
Segment
 aka line segment; the set of points consisting of two distinct points and all inbetween them; written
Semicircle
 an arc whose central angle is a right angle
Septagon
 a sevensided polygon
Set
 a collection of objects called elements
Side of a polygon
 a single segment from the union that forms a polygon
Similar figures
 two figures that have a similarity transformation mapping one onto the other; written F G
Similarity transformation
 a transformation that is the composite of size changes and/or reflections
Size change
 Let A be a point and k be a positive real number. For any point B, let T(B) = B’ be the point on with OP’ = K*OP. Then S is the size change with center A and magnitude k. See transformation.
Size change factor
 size change magnitude
Size transformation
 see size change
Skew lines
 noncoplanar lines that don’t intersect
Slant height
 the length of a lateral edge of a conic solid
Slide
 see translation
Slope
 the measure of the tilt of a line; rise over run (i.e., how much the line moves up for every movement to the right). The formula for slope is
y2y1
x2x1
Small circle
 the circle formed by the intersection of a sphere and a plane that doesn’t contain the center
Solid
 the union of the surface and the region of space enclosed by a 3D figure; examples: conic solid, cylindric solid, rectangular solid
Solid geometry
 the study of figures in threedimensional space
Space
 the set of all possible points; made up of infinite planes
Sphere
 the set of points in space equidistant from a certain point
Square
 an equilateral and equianglular quadrilateral
Straight angle
 an angle whose measure is 180 degrees, forming a line with its sides
Straightedge, unmarked
 just how it sounds, an unmarked tool used to draw straight lines
Subroutine
 a previously known algorithm used in another algorithm
Subset
 a set that is part of a larger set
Sufficient condition
 a version of a conditional that tells you when you can use the term defined, where the term is in the consequent; a condition that implies a preset conclusion; see meaning
Supplementary angles
 2 angles whose measures, when added together, equal 180 degrees
Surface
 the boundary of a 3D figure
Surface area
 the total area of the surface of a solid
Symmetry diagonal
 the diagonal that perpendicularly bisects the other and is a symmetry line for the kite
Symmetry line
 the line of reflection in a reflectionsymmetric figure
Terminal side
 the side that the measurement of an angle ends at
Tesselate
 the ability of a region to tessalate
Tesselation
 a covering of a plane with congruent copies of the same region with no holes or overlaps
Tetragon
 a foursided polygon; see quadrilateral
Theorem
 important mathematical statements which can be proven by postulates, definitions, and/or previously proved theorems
Threedimensional
 having length, width, and thickness (i.e., space)
3D figure
 a set of points in space; examples: box, cone, cylinder, parallelpiped, prism, pyramid, regular pyramid, right cone, right cylinder, right prism, sphere,
Tilt
 the measure of an angle as compared to a horizontal line; what happens when you kick the pinball machine too hard; see grade
Torus
 a 3D figure formed by rolling a rectangle into a cylinder and bending the cylinder until its bases meet; a “doughnut”; see net
Transformation
 a correspondence between two sets of points such that each point in the preimage has a unique image and that each point in the image has exactly one preimage; see reflection, size change, isometry, composite
Transformation notation
 T(P), which stands for the transformation of P; also Sk where the transformation S that maps (x, y) onto (kx, ky) and k is the magnitude of that transformation
Translation
 the composite of two reflections over parallel lines; aka slide
Transversal
 a line that intersects 2 others
Transversible
 a network in which all arcs can be traced without going over one more than once
Trapezoid
 a quadrilateral that has at least one pair of parallel sides; see isoscoles trapezoid
Triangle
 a polygon with three sides; see equilateral triangle, isoscoles triangle, right triangle, scalene triangle
Triangulate
 to divide a polygon into triangles
Tridecagon
 a 13sided polygon
Trigon
 a threesided polygon; see triangle
Twodimensional
 having both width and length, but no thickness
Undecagon
 an elevensided polygon
Union of two sets A and B
 the set of elements in A, B, or both; written AUB
Unit cube
 unit of measuring volume
Universal statement
 a conditional that uses the words ‘all’ or ‘everything’
Universe
 in a Venn diagram, everything that is outside the sets
Vanishing line
 the horizon; in a drawing it is at the height of viewer’s eye
Vanishing point
 the point in space where two parallel lines seem to meet
Vertex
 see node
Vertex angle
 the angle formed by the equilateral sides of an isoscoles triangle
Vertex of an angle
 the common endpoint of the two rays
Vertex of a conic solid
 the point that marks the thinnest part of a conic solid
Vertex of a polygon
 an endpoint of a segment in a polygon
Vertical angles
 2 angles that share a common vertex and whose sides form 2 lines
Vertical line
 a line that goes straight up and down, and whose slope is defined as infinite or undefined
View
 a drawing of a side of an object
Volume
 the amount of space a 3D object can hold
Wedge
 see sector
Zero angle
 an angle whose measure is 0. In a zero angle, both the initial and terminal sides are the same.
Zerodimensional
 having no dimension; a point
