Geometry Glossary Essay Research Paper Geometry GlossaryAcute

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


- 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


- 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


- not stable; changing

Analytic geometry

- see coordinate geometry


- 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


- the ‘if’ part of a conditional; represented by p; aka hypothesis, given, problem; see consequent


- the amount of space taken up in a plane by a figure


- 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


- the area of figure F

Automatic drawer

- a computer program that lets you build constructions


- the line containing the vertex of a conic solid and the center of the 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


- 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


- a surface made up of rectangles; a rectangular parallelpided


- 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


- the set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides


- when on a search, circling back to a previous place visited (definition, web site, etc.), usually unhelpful or redundant


- the perimeter of a circle


- 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)


- in the same line


- 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


- see nonconvex

Concentric circles

- circles that share the same center, but have different radii


- a statement that tells if one thing happens, another will follow; written as pq; see antecedent, consequent, converse, inverse, contrapositive


- the surface of a conic solid whose base is a circle; see right cone

Congruence tranformation

- see isometry


- 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


- 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


- 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


- a precise way of drawing which allows only 2 tools: the straightedge and the compass


- a size change where k is less than 1


- a type of conditional; if not q, then not p; written q p; see inverse


- 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


- 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.


- 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


- 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


- 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


- 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


- a ten-sided polygon


- unit used to measure angles

Dense line

- the line that contains the shortest path between two points


- 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


- see size change


- see size change


- the width, length, and height of a plane or space figure


- 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


- the distance between points A and B is written as AB

Distance between 2 parallel lines

- the length of a perpendicular segment between them


- a twelve-sided polygon


- a description of a point in which the point has a definite size


- a twelve-sided polygon


- a freehand picture using any tool; see construction


- 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


- a nine-sided polygon


- having angles of the same measure


- the same distance from something


- 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’


- 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


- in the proportion , a and d; see means


- a polygonal region of a surface

Family tree

- hierarchy; tower or pyramid of power or importance


- 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,


- 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


- 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


- a tesselation of congruent squares sometimes used to measure distance

Harmonic mean

- two times the product divided by the sum of the two numbers


- half of a sphere


- a seven-sided polygon


- a six-sided polygon

Hidden lines

- broken lines used to signify lines that normally wouldn’t be seen in a drawing


- a chart that shows varying levels of importance

Horizontal line

- a line whose slope is zero


- the side opposite the right angle in a right triangle


- 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


- if and only if; see biconditional

If-then statement

- see conditional


- 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


- 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


- 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


- 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


- a quadrilateral that has two distinct pairs of consecutive equilateral sides


- 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


- the actual area of a region


- 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


- one of the four main description of a point


- the set that satisfies a given condition


- 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


- making a transformation


- arrangement of pixels


- average


- a version of a conditional that defines a term, where the term is in the antecedent; see sufficient condition


- in the proportion , b and c; see extremes


- 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.


- the segment connecting the vertex of an angle in a triangle to the midpoint of the side opposite it


- 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


- a 2-D figure that can be folded on its segments or curved on its boundaries to form a 3-D figure; see article here


- a group of nodes and arcs


- a polygon with n sides


- a description of a point in a network where it is possible for two different segments to share the same endpoints


- a nine-sided 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

Non-Euclidean geometry

- solid geometry

Non-included side

- the side of a triangle that is not included by 2 given angles

Non-overlapping regions

- regions that don’t share interior points

Nonperspective drawing

- a three-dimensional drawing that doesn’t use perspective

Null set

- a set with nothing in it

Number line

- a coordinatized line

Oblique prism or cylinder

- a non-right 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


- an eight-sided polygon

Odd node

- a node with an odd number of arcs


- 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)


- 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)


- a quadrilateral with both pairs of opposite sides parallel


- a prism whose opposite faces are all parallelograms and congruent (in pairs)

Parallel planes

- planes that have no points in common


- a 15-sided polygon


- a five-sided 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


- feeling of depth

Perspective drawing

- a drawing in which, in order to show perspective, oblique parallel lines will meet


- 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


- small dot of color that makes up computer and TV screens


- a two-dimensional 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 two-dimensional figures in a plane

Plane section

- the intersection of a figure with a plane


- a zero-dimensional 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


- 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


- a three-dimensional surface which is the union of polygonal regions and has no holes


- a statement assumed to be true without proof; see theorem


- the original object that is reflected


- the surface of a cylindric solid whose base is a polygon; see right prism, parallelpiped, box


- a sequence of justified conclusions used to prove the validity of an if-then statement

Proper subset

- a subset that doesn’t include everything in its parent set; see improper subset


- a statement that two ratios are equal


- one of four numbers that form a true proportion


- a tool used to measure angles


- the goal of a proof


- 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


- “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.


- “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.


- a four-sided polygon; see quadrilateral

Quadratic equation

- Ax2 + By + C = 0

Quadratic term of an equation

- the term Ax2 in a quadratic equation


- a four-sided polygon; see rhombus, parallelogram, square, rectangle, trapezoid, isoscoles trapezoid, kite


- rotation


- radius


- plural form of radius


- the segment whose endpoints are any point on a circle or sphere and its center; the length of that segment


- a ratio where the quantities are of different kinds; example: 60 miles per hour


- a quotient of 2 numbers

Ratio of similtude

- the ratio of the length of an image to the length of the preimage


- a one-dimensional 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


- 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.


- 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

Reflection-symmetric 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


- 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


- the density of pixels in a picture


- 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


- the composite of two reflections over intersecting lines


- 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


- part of a circle containing its center and an arc


- aka line segment; the set of points consisting of two distinct points and all inbetween them; written


- an arc whose central angle is a right angle


- a seven-sided polygon


- 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

- non-coplanar lines that don’t intersect

Slant height

- the length of a lateral edge of a conic solid


- see translation


- 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



Small circle

- the circle formed by the intersection of a sphere and a plane that doesn’t contain the center


- the union of the surface and the region of space enclosed by a 3-D figure; examples: conic solid, cylindric solid, rectangular solid

Solid geometry

- the study of figures in three-dimensional space


- the set of all possible points; made up of infinite planes


- the set of points in space equidistant from a certain point


- 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


- a previously known algorithm used in another algorithm


- 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


- the boundary of a 3-D 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 reflection-symmetric figure

Terminal side

- the side that the measurement of an angle ends at


- the ability of a region to tessalate


- a covering of a plane with congruent copies of the same region with no holes or overlaps


- a four-sided polygon; see quadrilateral


- important mathematical statements which can be proven by postulates, definitions, and/or previously proved theorems


- having length, width, and thickness (i.e., space)

3-D figure

- a set of points in space; examples: box, cone, cylinder, parallelpiped, prism, pyramid, regular pyramid, right cone, right cylinder, right prism, sphere,


- the measure of an angle as compared to a horizontal line; what happens when you kick the pinball machine too hard; see grade


- a 3-D figure formed by rolling a rectangle into a cylinder and bending the cylinder until its bases meet; a “doughnut”; see net


- 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


- the composite of two reflections over parallel lines; aka slide


- a line that intersects 2 others


- a network in which all arcs can be traced without going over one more than once


- a quadrilateral that has at least one pair of parallel sides; see isoscoles trapezoid


- a polygon with three sides; see equilateral triangle, isoscoles triangle, right triangle, scalene triangle


- to divide a polygon into triangles


- a 13-sided polygon


- a three-sided polygon; see triangle


- having both width and length, but no thickness


- an eleven-sided 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’


- 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


- 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


- a drawing of a side of an object


- the amount of space a 3-D object can hold


- see sector

Zero angle

- an angle whose measure is 0. In a zero angle, both the initial and terminal sides are the same.


- having no dimension; a point


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