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 2-D figure that can be folded on its segments or curved on its boundaries to form a 3-D figure; see article here
Network
- a group of nodes and arcs
N-gon
- 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 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
Octagon
- an eight-sided polygon
Odd node
- a node with an odd number of arcs
One-dimensional
- 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 15-sided polygon
Pentagon
- 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
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 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
Point
- 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
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 three-dimensional 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 if-then 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 four-sided polygon; see quadrilateral
Quadratic equation
- Ax2 + By + C = 0
Quadratic term of an equation
- the term Ax2 in a quadratic equation
Quadrilateral
- a four-sided 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 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
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
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
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 seven-sided 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
- non-coplanar 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
y2-y1
x2-x1
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 3-D figure; examples: conic solid, cylindric solid, rectangular solid
Solid geometry
- the study of figures in three-dimensional 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 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
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 four-sided polygon; see quadrilateral
Theorem
- important mathematical statements which can be proven by postulates, definitions, and/or previously proved theorems
Three-dimensional
- 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,
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 3-D 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 13-sided polygon
Trigon
- a three-sided polygon; see triangle
Two-dimensional
- having both width and length, but no thickness
Undecagon
- 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’
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 3-D 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.
Zero-dimensional
- having no dimension; a point