Geometry Encyclopedia

Geometry Encyclopedia

If you would like to prepare for school subjects or simply increase your general knowledge, then enjoy our geometry encyclopedia. We tried to focus only on very important terms and definitions. We also kept our terminology very brief so that you absorb the concept more quickly and easily.

Geometry Glossary (Page 1)

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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,.
45-45-90 TRIANGLE: An isoscoles right triangle.
ACUTE ANGLE: An angle whose measure is greater than 0 but less than 90 degrees.
ADJACENT ANGLES: 2 nonstraight and nonzero angles that have a common side in the interior of the angle formed by the noncommon sides.
ALTERNATE EXTERIOR ANGLES: Exterior angles on alternate sides of the transversal (not on the same parallel line).
ALTERNATE INTERIOR ANGLES: Interior angles on alternate sides of the transversal (not on the same parallel line).
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 SIDE: One of the two rays forming an angle.
ANNULUS: A ring; the area bounded by two concentric circles.
ANTECEDENT: The 'if' part of a conditional; represented by p; aka hypothesis, given, problem; see consequent.
APOTHEM: In a regular polygon, the perpendicular distance from the center to a side; in a circle with a chord, the distance from the midpoint of a chord to the circle's center.
ARBELOS: A plane region bounded by three mutually tangent semicircles whose diameters are collinear.
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: The amount of space taken up in a plane by a figure.
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.
BALL: A "solid sphere"; the interior of a sphere (open ball); a sphere and its interior (closed ball);.
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.
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.
BORROMEAN RINGS: A set of three rings joined in such a way that no pair is interlinked, but the three cannot be separated.
BOX: A surface made up of rectangles; a rectangular parallelpided.
BUNDLE: The set of planes through a point, in projective geometry.
CAGE: Regular graph that has as few vertices as possible for its girth. Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. The (r,3)-cage is a complete graph Kr+1 on r+1 vertices, and the (r,4)-cage is a complete bipartite graph Kr,r on 2r vertices. Other cages listed in Wikipedia include the Moore graphs: (3,5)-cage: Petersen graph, (3,6)-cage: Heawood graph, (3,8)-cage: Tutte Coxeter graph, (7,5)-cage: Hoffman Singleton graph.
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.
CEVIAN: A line segment connecting a vetex of a triangle with a point on the opposite side of the triangle. The condition for three general Cevians from the three vertices of a triangle to concur (at a cevian point) is known as Ceva's theorem.
CEVIAN POINT: The point of concurrence of three cevians.
CEVIAN TRIANGLE: Given a point P and a triangle ABC, the Cevian triangle A'B'C' is defined as the triangle composed of the endpoints of the cevians through the Cevian point P.
CHORD: In general, a straight line joining two points on a curve; often, chord is used to mean a straight line segment joining and included between two points on a 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.
CIRCULAR: Having the shape of a circle; a circular cylinder is one in which its defining shape is a circle, and most often is used to mean a right circular cylinder; a circular cone is one in which its defining shape is a circle, and most often is used to mean a right circular cone;.
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.
COMPLEX POLYGON: A polygon having at least one pair of intersecting edges; as opposed to simple; reflex polygon.
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)).
CONCAVE: See nonconvex.
CONCAVE SET: A set of points in which not all segments connecting points of the set lie entirely in the set; nonconvex.
CONCENTRIC: Having the same center, as concentric circles; having the same axis, as concentric cylinders.
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 p q; 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.
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.
CONSTANT WIDTH: Of a bounded figure: having the same width in every direction. A Reuleaux triangle is an example of a figure of constant width. Other examples include the shape formed by an equilateral triangle of side s with circles of radius r around each vertex, and arcs of radius s+r centered on the "far" vertices that join these circles. The same construction can be made with an equilateral (but not necessarily equiangular n-sided star, with n an odd number. .
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 p => q, than its converse is q => p.
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.
CYCLIC QUADRILATERAL: A quadrilateral whose four vertices lie on a circle.
CYCLOGON: A curve traced by any vertex of a regular polygon that rolls without sliding on a straight line. If the "vertices" of the cyclogon were linked by straight lines instead of curved ones, then the area under one arch of that figure would be three times the area of the regular polygon.
CYCLOID: A curve traced by any point on the circumference of a circle that rolls without sliding on a straight line. A curtate cycloid is a curve generated in the same way, except that the point is inside the circle rather than on the circle. A prolate cycloid is a curve generated in the same way, except that the point is rigidly fixed outside the circle. All cycloids, including curtate and prolate cycloids, are trochoids.
CYLINDER: The surface of a cylindric solid whose base is a circle; see right cylinder.
CYLINDRIC SOLID: The set of points between a region and its translation in space, including the region and its image.

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