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Geometry Glossary Essay Research Paper Geometry GlossaryAcute (стр. 1 из 2)

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