Appendix D: Glossary of Geometric and Mathematical Terms
For additional definitions of geometry and measurement terms, visit the Web sites of the Visual Geometry Dictionary for Kids and for Kids' Teachers (http://www.math.okstate.edu/%7Erpsc/dict/Dictionary.html) and the Maths Thesaurus (http://thesaurus.maths.org). Also see Christine G. Renne's article, "Is a Rectangle a Square? Developing Mathematical Vocabulary and Conceptual Understanding," Teaching Children Mathematics 10, no. 5 (2004): pp. 258-63.
Acute angle: An angle that measures between 0 and 90 degrees
Acute triangle: A triangle with three acute angles
Adjacent angles: Two angles on a plane that share a common vertex and a common side
Adjacent sides: In a polygon, two sides that share a common endpoint
Algorithm: A step-by-step procedure used for solving a problem
Alternate exterior angles: When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and outside the parallel lines, and the angles in each pair are congruent
Alternate interior angles: When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and inside the parallel lines, and the angles in each pair are congruent
Altitude: Height; the perpendicular distance from a vertex of a polygon to its opposite side
Analytic geometry: Geometry that deals with the relation between algebra and geometry, using graphs and equations of lines, curves, and surfaces to develop and prove relationships
Angle: The union of two rays with the same endpoint (its vertex); the amount of rotation of a ray about a fixed ray
Apex: The point off the base of a pyramid where the triangular sides meet
Arc: A part of a circle; the set of points on the circle between two points on the circle, plus those two endpoints arc
Area: The number of square units in a closed two-dimensional or plane shape
Axiom: A basic assumption that is accepted without proof
Axis: One of the number lines that form a coordinate system
Axis of symmetry: A line that divides a shape into two congruent halves
Base: The side of a shape used as the foundation for the shape; the face of a solid used as the foundation for the solid
Bisect: To cut something (such as a line segment or an angle) into two equal parts
Bisector: A straight line that divides an object into two equal parts
Capacity: The amount a container will hold such as fluid ounces or liters
Cartesian coordinate system: See Coordinate plane
Center of a circle: A fixed point equidistant from all points on the circle
Center of rotation: The only point in the plane that remains unchanged under a rotation of the plane
Chord: A line segment joining two points on a circle
Circle: A set of all points in a plane that are the same distance (radius) from a fixed point (center)
Circular cone: A three-dimensional shape with one circular base and a vertex that is not in the same plane as the base
Circumference: The perimeter of a circle
Clockwise rotation: Rotation about a point in a clockwise direction
Collinear points: Three or more points on the same line in a plane or in space
Collinear rays: Two rays that are subsets of the same line in a plane or in space
Compass: A tool used to draw circles of different radii or mark off equal lengths
Complementary angles: Two angles for which the sum of their measures is 90 degrees
Concave (non-convex): A shape with the property that the line segment connecting any two interior points is not totally contained in the shape; Not convex
Congruence: The relationship between two geometric shapes having the same size and shape (congruent shapes)
Contraction: See Dilation
Convex shape: A shape with the property that the line segment connecting any two interior points is contained in the shape
Coordinate: On a number line, the number paired with a point. In the coordinate plane, the numbers which are paired with a point. Point (2,4) has x-coordinate 2 and y-coordinate 4.
Coordinate plane: The number plane formed by two perpendicular number lines that intersect at their zero points (also called the Cartesian coordinate system)
Corollary: A statement that is readily proved deductively by applying a theorem
Corresponding angles: When two parallel lines are cut by a transversal, the pairs of angles that are on the same side of the transversal (one inside the parallel lines and one outside the parallel lines) and are congruent
Corresponding parts (angles and sides): Angles and sides in the same position on two shapes. In congruent shapes, the corresponding angles and sides are congruent.
Counterclockwise rotation: Rotation about a point opposite the rotation of a clock hand
Cube: A rectangular polyhedron composed of six congruent squares
Cylinder: A solid shape whose bases are formed by congruent circles in parallel planes and whose lateral surface is curved. The segment whose endpoints are the centers of the circular bases is called the axis of the cylinder. The altitude is a segment perpendicular to the base planes with an endpoint in each plane.
Decagon: A polygon of ten sides
Definition: A statement that gives the meaning of a word or symbol in terms that have been previously defined or are accepted as undefined
Degree: The standard unit for angle measure; one revolution is 360 degrees; a unit for measuring temperature
Diagonal: A segment connecting two non-adjacent vertices of a polygon diagonal
Diameter: A chord containing the center of a circle or sphere; the segment whose endpoints are points on a circle (or sphere) that contains the center of the circle (or sphere) as its midpoint
Dilation: A transformation in which each point P in the plane is mapped to a point P' on the ray OP where O is a fixed point in the plane. The position if P' is determined by the scale factor k by choosing P' so OP' = k OP. If k is less than one the transformation is called a contraction. Informally, a dilation transforms a polygon to a similar shape in which the sides are proportional.
Dimensions: Length, width, and/or height of a plane or solid shape
Edge: The line of a three-dimensional shape where two plane faces meet
Equiangular: A term used to indicate that all angles of a polygon have the same measure
Equilateral: A term used to indicate that all the sides of a polygon are equal in length
Euclidean geometry: The geometry (plane or solid) based on Euclid's postulates
Euler's formula: The relationship between the number of vertices, the number of faces, and the number of edges of any polygon (V + F = E + 2)
Face: One of the plane surfaces of a polyhedron bounded by edges
Function in two variables: A set of ordered pairs (x, y) in which each value of x is paired with exactly one value of y
Geometry: The study of space and properties of shapes in space
Glide reflection: A transformation that consists of a translation parallel to a fixed line followed by a reflection about the line
Hexagon: A polygon of six sides
Hypotenuse: The side in a right triangle that is opposite the right angle hypotenuse
Image: The shape formed by a transformation of a shape (the pre-image)
Interior angles: Angles on the inside of a shape
Intersecting lines: Two different lines that contain exactly one point in common
Isometric drawing: A drawing where length, width, and height are represented by lines 120 degrees apart, with all measurements in the same scale
Isosceles trapezoid: A quadrilateral with one pair of sides that are parallel and another pair of sides that are not parallel but have equal lengths; the base angles are equal in measurement.
Isosceles triangle: A triangle with two congruent sides
Kite: Quadrilateral with two distinct pairs of adjacent sides that are congruent
Lattice point: A point in a coordinate plane with integer coordinates
Leg: In a right triangle, a side that is not the hypotenuse
Lemma: A theorem proven only for use in the proof of more important theorems
Length of a segment: The distance between the endpoints of a segment
Line: An undefined term for an infinite, one-dimensional object
Line of reflection: A line used to create a reflection of a shape
Line segment: Part of a line consisting of two endpoints and all the points on the line between them
Line of symmetry: A line that divides a shape into two congruent halves
Midpoint: A point that divides a line segment into two congruent segments
Net of a polyhedron: A pattern that can be cut out, folded, and glued together to make a three-dimensional model of a solid
Network: A set of vertices and edges
Non-collinear points: Points that do not lie on the same line
Non-Euclidean geometry: Any geometry that changes at least one of Euclid's postulates
Number line: A line with an origin (0) and a unit length that allows for each integer to be assigned a point in the line
Obtuse angle: An angle with measure of between 90 and 180 degrees
Obtuse triangle: A triangle with one interior angle that is obtuse
Octagon: A polygon of eight sides
One-dimensional: Having length but no width, e.g., lines, rays, and segments
Ordered pair: A pair of numbers in which the order is specified, used to locate a point in a coordinate plane
Origin: On the coordinate plane the point where the two perpendicular lines (axes) intersect or the point (0,0)
Parallel lines: Lines in the same plane that do not intersect
Parallel planes: Two planes in three-dimensional space that never meet
Parallelogram: A quadrilateral with opposite sides that are parallel
Pentagon: A polygon with five sides
Pentomino: Five equal-sized squares that can be attached edge-to-edge to form a three-dimensional shape
Perimeter of a polygon: The sum of the lengths of all sides of a polygon; the distance around a closed plane shape
Perpendicular: Forming a right angle
Pi: The ratio of the circumference of a circle to its diameter
Pick's theorem: Given a polygon where each vertex is on a pin of a geoboard, the area can be found by the formula A = B/2 + I - 1, where B is the number of boundary points and I is the number of interior points.
Plane: An undefined term for a flat, infinite two-dimensional shape
Plane geometry: The geometry that deals with shapes in a two-dimensional plane
Platonic solids: See regular polyhedron
Point: A location on a line, in a coordinate plane, or in space; an undefined term for a zero-dimensional object (having no length, width, or height)
Polygon: A simple closed shape composed of a finite number of line segments, each of which intersects exactly two of the other segments, one at each endpoint
Polyhedron: A simple closed three-dimensional shape formed by plane polygons
Postulate: A basic assumption that is accepted without proof
Prism: A polyhedron that has two congruent parallel faces and a set of parallel edges that connect corresponding vertices of the two faces
Protractor: A tool used to measure angles
Pyramid: A polyhedron that has one base and a set of edges that meet at a single point (apex) that is not in the base; all faces except the base are triangles
Pythagorean theorem: A theorem that states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the sides.
Quadrant: Any one of the four regions into which a plane is divided by a pair of coordinate axes
Quadrilateral: A polygon with four sides
Radius: A line segment connecting the center of a circle (or sphere) to any point on the circle (or sphere); the length of that line segment
Ray: A part of a line with a single endpoint and that extends infinitely in one direction
Rectangle: A quadrilateral with all interior right angle
Reflection (flip): A transformation that maps each point in a plane to a new point that is the same distance from a fixed line (called the line of reflection) but on the opposite side of the line; informally, a geometric shape that can be flipped over a line so that the new shape is a mirror image of the original
Regular polygon: A polygon that is equilateral and equiangular
Regular polyhedron: A polyhedron whose faces are congruent regular polygons and where each vertex figure (how the polygons meet at a vertex) is identical; also called a Platonic solid
Rhombus: A parallelogram with four congruent sides
Right angle: An angle with a measure of 90 degrees
Right triangle: A triangle that has a right angle
Rotation (turn): A transformation that maps every point in a plane shape to its image by rotating the plane through an angle (called the turn angle) around a fixed point (called the turn center or center of rotation)
Rotational symmetry: A term that describes a shape that remains unchanged when it is turned less than 360 degrees about a fixed point
Scalene triangle: A triangle with no two sides of the same length
Segment: A set of points containing two endpoints and all points along the straight line between the two endpoints; a part of a circle between an arc and its chord
Semicircle: Half of a circle
Set: A group of objects or numbers, which are called elements of the set
Similar shapes: Two shapes that have the same shape-corresponding angles that are congruent and corresponding sides that are proportional
Simple closed curve: A set of points in a plane that can be drawn such that the initial and final points are the same and the curve never intersects itself; it divides the plane into three regions: the region inside the curve, the curve, and the region outside the curve.
Simple closed surface: A surface without holes that encloses a hollow region; it divides space into three regions: the region interior to the surface, the surface, and the region exterior to the surface.
Slide: See translation
Solid geometry: Geometry that deals with shapes and their properties in three-dimensional space
Sphere: A shape in space whose points are the same distance from a fixed point (the center)
Spherical geometry: Geometry that deals with shapes on the surface of the sphere
Square: An equilateral and equiangular quadrilateral
Straight angle: An angle with measure of 180 degrees
Supplementary angles: Two angles for which the sum of their measures is 180 degrees
Surface area: The total area of the outside of a three-dimensional shape
Symmetry: Correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis
Synthetic geometry: Geometry that explores properties of geometric objects without algebra
Tangram: A Chinese puzzle made up of a square cut into seven pieces that can be rearranged to make various shapes
Tessellation: A repetitive pattern of polygons that covers (or tiles) a plane with no gaps and no overlaps
Tetrahedron: A polyhedron with four faces
Theorem: A statement that can be proven using logical (deductive) reasoning
Three-dimensional: Having length, width, and thickness
Transformation of the plane: A one-to-one correspondence that maps each point P (called the preimage) in the plane to a point P' (called the image) in the plane
Translation (slide): A transformation of a plane where every point P is moved in the same direction and the same distance to a new point P'; moving a shape along a straight line without it flipping, rotating, or reflecting
Transversal: A straight line that crosses two or more given lines
Trapezoid: A quadrilateral with exactly one pair of parallel sides
Triangle: A polygon with three sides
Two-dimensional: Having both length and width, but no thickness
Undefined term: A term-such as point, line, plane, and space-that is accepted without definition
Vertex: The point where two rays forming an angle meet, the point where two sides of a polygon meet, or the point where three or more faces of a polygon meet
Vertical angles: A pair of non-adjacent angles formed by intersecting lines; also called vertically opposite angles
Volume: Amount of space enclosed by a simple closed surface, measured in cubic units
X-axis: The horizontal number line in a plane
Y-axis: The vertical number line in a coordinate plane
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