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1.Angle Two rays sharing a common endpoint. Angles are typically measured in degrees or radians. Angle 2.Acute Angle An angle that has measure less than 90°. 3.Adjacent Angles Two angles in a plane which share a common vertex and a common side but do not overlap. Angles 1 and 2 below are adjacent angles. Adjacent Angles 4.Apothem The line segment from the center of a regular polygon to the midpoint of a side, or the length of this segment. Same as the inradius; that is, the radius of a regular polygon's inscribed circle. Note: Apothem is pronounced with the emphasis on the first syllable with the a pronounced as in apple (A-puh-thum). 5.Base In plane geometry or solid geometry, the bottom of a figure. If the top is parallel to the bottom (as in a trapezoid or prism), both the top and bottom are called bases. 6.Chord A line segment on the interior of a circle. A chord has both endpoints on the circle. 7.Centroid For a triangle, this is the point at which the three medians intersect. In general, the centroid is the center of mass of a figure of uniform (constant) density. 8.Circle The locus of all points that are a fixed distance from a given point. 9.Circumference A complete circular arc. Circumference also means the distance around the the outside of a circle. 10.Collinear Lying on the same line. 11.Concave Non-Convex A shape or solid which has an indentation or "cave". Formally, a geometric figure is concave if there is at least one line segment connecting interior points which passes outside of the figure. 12.Cone A three dimensional figure with a single base tapering to an apex. The base can be any simple closed curve. Often the word cone refers to a right circular cone. 13.Congruent Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent. Note: Congruent segments, sides, and angles are often marked. Congruent Segments Congruent Angles All four sides of this rhombus are marked to show they are congruent to each other. The marked angles of this isosceles triangle are congruent to each other. 14. Contrapositive Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining." 15.Convex A geometric figure with no indentations. Formally, a geometric figure is convex if every line segment connecting interior points is entirely contained within the figure's interior. 16.Coplanar Lying in the same plane. For example, any set of three points in space are coplanar. 17.Corresponding Two features that are situated the same way in different objects. 18.Cube Regular Hexahedron A regular polyhedron for which all faces are squares. Note: It is one of the five platonic solids. Cube a = length of an edge Volume = a3 Rotate me if your browser is Java-enabled. Surface Area = 6a2 19.Cylinder A three-dimensional geometric figure with parallel congruent bases. The bases can be shaped like any closed plane figure (not necessarily a circle) and must be oriented identically. Note: The word cylinder often refers to a right circular cylinder. 20.Decagon A polygon with ten sides. Decagon Regular Decagon 21.Degree A unit of angle measure equal to of a complete revolution. There are 360 degrees in a circle. Degrees are indicated by the ° symbol, so 35° means 35 degrees. 22.Diameter of a Circle or Sphere A line segment between two points on the circle or sphere which passes through the center. The word diameter is also also refers to the length of this line segment. 23.Distance Formula is the distance between points (x1, y1) and (x2, The formula y2). 24.Dodecagon A polygon with 12 sides. Dodecagon Regular Dodecagon 25.Dilation A transformation in which a figure grows larger. Dilations may be with respect to a point (dilation of a geometric figure) or with respect to the axis of a graph (dilation of a graph). Note: Some high school textbooks erroneously use the word dilation to refer to all transformations in which the figure changes size, whether the figure becomes larger or smaller. Unfortunately the English language has no word that refers collectively to both stretching and shrinking. Pronunciation: Dilation (die-LAY-shun) has only three syllables, not four 26.Dodecahedron Regular Dodecahedron A polyhedron with 12 faces. A regular dodecahedron has faces that are all regular pentagons. Note: It is one of the five platonic solids. Regular Dodecahedron a = length of an edge Rotate me if your Volume = browser is Java-enabled. Surface Area = 27.Edge of a Polyhedron One of the line segments making up the framework of a polyhedron. The edges are where the faces intersect each other. 28.Equidistant Equally distant. For example, any two points on a circle are equidistant from the center. 29.Equilateral Triangle A triangle with three congruent sides. Note: The angles of an equilateral triangle are each 60°. Equilateral Triangle s = length of a side 30.Euler's Formula (Polyhedra) The equation below: (number of faces) + (number of vertices) – (number of edges) = 2 This formula is true for all convex polyhedra as well as many types of concave polyhedra. Note: Euler is pronounced "Oiler". 31.Evaluate To figure out or compute. For example, "evaluate out that the expression simplifies to 17. " means to figure 32.Exterior Angle of a Polygon An angle between one side of a polygon and the extension of an adjacent side. Note: The sum of the exterior angles of any convex polygon is 360°. This assumes that only one exterior angle is taken at each vertex. 33.Face of a Polyhedron One of the flat surfaces making up a polyhedron. Note: The faces of a polyhedron are all polygons. 34.Formula An expression used to calculate a desired result, such as a formula to find volume or a formula to count combinations. Formulas can also be equations involving numbers and/or variables, such as Euler's formula. 35.Geometry The study of geometric figures in two dimensions (plane geometry) and three dimensions (solid geometry). It includes the study of points, lines, triangles, quadrilaterals, other polygons, circles, spheres, prisms, pyramids, cones, cylinders, and polyhedra. Geometry typically includes the study of axioms, theorems, and two-column proofs. Among the various types of geometry are analytic geometry, Euclidean geometry, and non-Euclidean geometry 36.Height The shortest distance between the base of a geometric figure and its top, whether that top is an opposite vertex, an apex, or another base. 37.Height of a Cone The distance from the apex of a cone to the base. Formally, the shortest line segment between the apex of a cone and the (possibly extended) base. Altitude also refers to the length of this segment. 38.Height of a Cylinder The distance between the bases of a cylinder. Formally, the shortest line segment between the (possibly extended) bases. Altitude also refers to the length of this segment. 39.Height of a Prism The distance between the two bases of a prism. Formally, the shortest line segment between the (possibly extended) bases. Altitude also refers to the length of this segment. 40.Hexagon A polygon with six sides. Hexagon Regular Hexagon 41.Altitude of a Triangle Height of a Triangle The distance between a vertex of a triangle and the opposite side. Formally, the shortest line segment between a vertex of a triangle and the (possibly extended) opposite side. Altitude also refers to the length of this segment. Note: The three altitudes of a triangle are concurrent, intersecting at the orthocenter. 42.Heptagon A polygon with seven sides. Some authors also use the name septagon instead of heptagon. Heptagon Regular Heptagon 43.Hypotenuse The side of a right triangle opposite the right angle. Note: The hypotenuse is the longest side of a right triangle. 44.Interior Angle An angle on the interior of a plane figure. Examples: The angles labeled 1, 2, 3, 4, and 5 in the pentagon below are all interior angles. Angles 3, 4, 5, and 6 in the second example below are all interior angles as well (parallel lines cut by a transversal). Note: The sum of the interior angles of an n-gon is given by the formula (n – 2)·180°. For a triangle this sum is 180°, a quadrilateral 360°, a pentagon 540°, etc. 45.Isosceles Trapezoid A trapezoid with base angles that are the same. Consequently, the legs will be congruent to each other as well. 46.Isosceles Triangle A triangle with two sides that are the same length. Formally, an isosceles triangle is a triangle with at least two congruent sides. 47.Lateral Surface Area Lateral Area The surface area of the lateral surfaces of a solid. Lateral surface area does not include the area of the base(s). 48.Lateral Surface Lateral Face The face or surface of a solid on its sides. That is, any face or surface that is not a base. 49.Linear Pair of Angles A pair of adjacent angles formed by intersecting lines. Angles 1 and 2 below are a linear pair. So are angles 2 and 4, angles 3 and 4, and angles 1 and 3. Linear pairs of angles are supplementary. 50.Locus A word for a set of points that forms a geometric figure or graph. For example, a circle can be defined as the locus of points that are all the same distance from a given point. 51.Major Arc The longer of the two arcs between two points on a circle. 52.Midpoint Formula is the formula for the midpoint between points (x1, y1) and (x2, y2). Note that this is simply the average of the x-coordinates and the average of the y-coordinates. 53.Minor Arc The shorter of the two arcs between two points on a circle. 54.Nonagon A polygon with nine sides. Nonagon Regular Nonagon 55.Oblique Cylinder A cylinder with bases that are not aligned one directly above the other. 56.Oblique Pyramid A pyramid with an apex that is not aligned above the center of the base. Solid view: oblique pyramid with a square base Frame view: oblique pyramid with a square base h = height of the pyramid B = area of the base 57.Obtuse Angle An angle that has measure more than 90° and less than 180°. 58.Octagon A polygon with eight sides. Octagon Regular Octagon 59.Parallelogram A quadrilateral with two pairs of parallel sides. 60.Pentagon A polygon with five sides. Pentagon Regular Pentagon 61.Point The geometric figure formed at the intersection of two distinct lines. 62.Polyhedron A solid with no curved surfaces or edges. All faces are polygons and all edges are line segments. 63.Prism A solid with parallel congruent bases which are both polygons. The bases must be oriented identically. The lateral faces of a prism are all parallelograms or rectangles. 64.Pyramid A polyhedron with a polygonal base and lateral faces that taper to an apex. A pyramid with a triangular base is called a tetrahedron. Solid view: right regular pyramid with a regular Frame view: right regular pyramid with a regular pentagon as base pentagon as base 65.Quadrilateral Quadrangle A polygon with four sides. 66.Ray A part of a line starting at a particular point and extending infinitely in one direction. 67.Rectangle A box shape on a plane. Formally, a rectangle is a quadrilateral with four congruent angles (all 90°). 68.Regular Polygon A polygon for which all sides are congruent and all angles are congruent. Regular Polygon Formulas n = number of sides s = length of a side r = apothem (radius of inscribed circle) R = radius of circumcircle Regular Pentagon Regular Hexagon Sum of interior angles = (n – 2)·180° Interior angle = Area = (½)nsr Regular Heptagon Regular Octagon Regular 69.Right Angle A 90° angle. 70.Secant Line A line which passes through at least two points of a curve. Note: If the two points are close together, the secant line is nearly the same as a tangent line. 71.Line Segment Segment All points between two given points (including the given points themselves). Example: line segment 72.Solid Geometric Solid Solid Geometric Figure The collective term for all bounded three-dimensional geometric figures. This includes polyhedra, pyramids, prisms, cylinders, cones, spheres, ellipsoids, etc. 73.Supplementary Angles Two angles that add up to 180°. 74.Tangent Line A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line. Note: A line tangent to a circle is perpendicular to the radius to the point of tangency. 75.Vertex A corner point of a geometric figure. For a polygon, vertices are where adjacent sides meet. For an angle, the vertex is where the two rays making up the angle meet. Note: If the figure is a curve or surface, the vertices are the points of maximum curvature.