Geometry Flashcards
1
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A branch of mathematics that deals with the properties, measurement, and relationships of points, lines, angles, and solids, deduced from their defining conditions by means of certain assumed properties of space.
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Geometry
2
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A dimensionless geometric element that has no property but location, such as the intersection of two lines.
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Point
3
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The axis along which ordinates or y-values are measured in a Cartesian corrdinate system.
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Y-axis or Axis of Ordinates
4
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A coordinate determined by measuring parallel to the z-axis.
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Z-coordinate
5
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The axis along which values of z are measured in a three-dimensional Cartesian Coordinate system/
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Z-axis
6
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A coordinate determined by measuring parallel to the x-axis.
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Abscissa or X-coordinate
7
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Any of a set of numbers that serve to specify the location of a point on a line, surface, or in space by reference to a fixed figure or system of lines.
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Coordinate
8
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Any of the coordinates for locating a point on a plane by its distance from each of two intersecting lines, or in space by its distance from each of three planes intersecting at a point.
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Cartesian Coordinate
9
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A coordinate determined by measuring parallel to the y-axis.
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Ordinate or Y-coordinate
10
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A Cartesian coordinat esystem in which the axes or coordinate planes are perpendicular.
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Rectangular Coordinate System
11
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The axis along which abscissas or x-values are measured in a Cartesian coordinate system.
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X-axis or Axis of Abscissaas
12
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Geometry based upon the postulates of Euclid, esp. the postulate that only one line may be drawn through a given point parallel to a given line.
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Euclidean Geometry
13
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A straight line segment that joins a variable point to the fixed origin of a polar coordinate system.
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Radius Vector
14
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The angle formed by the polar axis and a radius vector in a polar coordinate system.
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Polar Angle
15
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The reference axis from which the polar angle is measured in a polar coordinate system.
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Polar Axis
16
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A system for locating a point on a plane by its radius vector and polar angle.
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Polar Coordinate System
17
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Extending in the same direction, equidistant at all points, and never converging or divergin.
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Parallel
18
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Any lines in space that are neither parallel nor intersecting.
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Skew Lines
19
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Perpendicular to the plane of the horizon.
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Vertical
20
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Neither parallel nor perpendicular to a given line or surface.
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Oblique
21
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A geometric element generated by a moving point and having extension without breadth or thickness.
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Line
22
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The space between two line diverging from a common point, or within two planes diverging from a common linel; the figure so formed.
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Angle
23
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The point at which the sides of an angle intersect.
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Vertex
24
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The amount of rotation needed to bring one line or plane into coincidence with another, measured in radians or in degress, minutes, and seconds.
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Angle
25
A unit of angular measure equal to the central angle subtending an arc equal in length to the radius. 360/2pie or approxiamately 57.3d.
Radian
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A unit of angular measure, equal to 1/360th of a complete angle or turn, or of the circumference of a circle.
Degree
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The 60th part of a degree of angular measure.
Minute
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The 60th part of aminute of angular measure.
Second
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An angle of 90d formed by the perpendicular intersection of two straight lines.
Right Angle
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An angle less than 90d.
Acute Angle
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An angle greater than 90d, but less than 180d.
Obtuse Angle
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Extent or distance upward from a given level to a fixed point.
Height
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The line or surface forming the part of a geometric figure that is most nearly horizontal or on which it is supposed to stand, from which an altitude can be constructed.
Base
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The point opposite to and farthest from the base of a plane figure.
Vertex
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The perpendicular distance from the base of a geometric fiture to the opposite vertex. Parallel side, or parallel surface.
Altitude
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Reentering or pointing inward, such as an interior angle of a polygon that is greater than 180d.
Reentrant
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A polygon having three sides and three angles.
Triangle
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An outward projecting angle or part.
Salient
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A polygon having four sides and four angles.
Quadrilateral
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The branch of geometry that deals with plane figures,
Plane Geometry
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A surface generated by a straight line moving at a constant velocity with respect to a fixed point, such that a straight line joining any two of its points lies wholly in the surface.
Plane
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A combination of geometric elements disposed in a particular form or shape.
Figure
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A closed plane figure having three or more straight sides.
Polygon
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Forming, formed by, or characterized by straight lines
Rectilinear
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Having edges, surfaces, or faces that meet at right angles.
Rectangular
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In any rectangular configuration, the ratio of the longer dimension to the shorter.
Aspect ratio
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A line connecting two nonadhacent angles or vertices of a polygon or polyhedron.
Diagonal
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A parallelogram having four right angles, esp. one with sides of unequal lengths.
Rectangle
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Having two sides of equal length
Isosceles
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Composed only of acute angles.
Acute
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Having an obtuse angle.
Obtuse
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Having three unequal sides.
Scalene
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Occupying the same place in space or time.
Coincident
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Coinciding at all points when superimposed.
Congruent
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having corresponding sides proportional and corresponing angles equal.
Similar
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The angle formed between any side of a polygon and an extended adjacent side.
Exterior Angle
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The angle formed inside a polygon between any two adjacent sides.
Interior Angle
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An oblique line or surface, as one formed by cutting off the corner of square or cube.
Cant
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A regular polygon having four equal sides and four right angles.
Square
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A quadrilateral having both pairs of opposite sides parallel to each other.
Parallelogram
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A quadrilateral having only two sides parallel.
Trapezoid
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A quadrilateral having no two sides parallel.
Trapezium
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The branch of mathematics that deals with the properties of triangles and trigonometric functions, and of their applications.
Trigonometry
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A function of an angle, as sine or cosine, expressed as the ratio of the sides of a right triangle.
Trigonometric Function
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The trigonometric function defines as the ratio of the side opposite a given angle to the hypotenuse.
Sine
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The trigonometric function defined as the ratio of the side adjacent to a given angle to the hypothenuse.
Coside
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The trigonometric function defined as the ratio of the side opposite a given angle to the side adjacent to the angle.
Tangent
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The trigonometric function defined as ratio of the hypotenuse to the side adjacent to a given angle.
Secant
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The trigonometric function defined as the ratio of the hypotenuse to the side opposite a given angle.
Cosecant
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The trigonometric function defined as the ratio of the side adjacent to a given angle to the side opposite the angle.
Cotangent
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A triangle having a right angle.
Right Triangle
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The side of a right triangle that is opposite the right angle.
Hypotenuse
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The theorem that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
Pythagorean Theorem
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A polygon having five sides and five angles.
Pentagon
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A polygon having six sides and six angles.
Hexagon
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A polygon having eight sides and eight angles.
Octagon
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A perpendicular from the center of regular polygon to one of its sides.
Apothem
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Having all sides qual (equilateral) and all angles equal (equiangular).
Regular
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A closed plane curve every point of which is equidistant from a fixed point within the curve.
Circle
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Any part of the circumference of a circle.
Arc
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A straight line extending from the center of a circle or sphere to the circumfrence or bounding surface.
Radius
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A plane figure bounded by two radii and the included arc of a circle.
Sector
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A straight line extending through the center of a circle or sphere and meeting the circumference or bounding surface at each end.
Diameter
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The point within a circle or sphere equally distant from all points of the circumference or surface, or the point within a regular polygon equally distant from the vertices.
Center
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The boundary line of a closed curvilinear figure, esp. the perimeter of a circle.
Circumference
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The symbol π denoting the ratio between the circumference of a circle and its diameter, a constant equal to 3.14159+
Pi
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Not having the same center or center line.
Eccentric
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Not centered or at the center [point.
Off-center
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Denoting circles, arcs, or spheres having a common center.
Concentric
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An imaginary line that bisects a plane figure.
Centerline
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An arc of 90d, or any of the four quarters into which a plane figure is divided by two perpendicular lines, numbered counterclockwise from the upper right.
Quadrant
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A continuously bending line, without angles.
Curve
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Curved inward like the interior of a circular arc or hollow sphere.
Concave
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A change of curvature from convex to concave or vice versa.
Inflection
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Curved or rounded outward like the exterior of a circle or sphere.
Convex
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A point where two branches of curve meet, end, and are tangent.
Cusp
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The straight line segment between two points on a given curve.
Chord
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Touching at a single point, such as a straight line in relation to a curve, or in contact along a single line, such as a plane with a cylinder.
Tangent
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Touching at a single point, such as a straight line in relation to a curve, or in contact along a single line, such as a plane with a cylinder.
Tangent
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A closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points, the foci, is a constant.
Ellipse
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The axis passing through the two foci of an ellipse.
Major Axis
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The axis of an ellipse that is perpendicular to the major axis at a point equidistant from the foci.
Minor Axis
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A plane curve generated by a point moving around a fixed point while constantly receding from or approaching it.
Spiral
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The locus of the centers of curvature of or the envelope of the normals to another curve.
Evolute
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A curve traced by a point on a string as it is kept taut and unwound from a stationary cylinder.
Involute
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A plane curve generated by a point so moving that it remains equidistant from a fixed line and a fixed point not on the line.
Parabola
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A plane curve generated by a point so moving that the differnece of the distances from two fixed points in the plane remains constant.
Hyperbola
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A straight line limiting a curve such that the perpendicular distance from the curve to the line approaches zero as the curve is extended to infinity.
Asymptote
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A three-dimensional curve traced on a cylinder or cone by the rotation of a point crossing its right sections at a constant oblique angle.
Helix
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A curve generated by a point on the circumference of a circle as it rolls along straight line.
Cycloid
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A solid geometrical figure similar in shape to a sphere, such as an ellipsoid.
Spheroid
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A solid figure all plane sections of which are ellipses.
Ellipsoid
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A spheroid generated by rotating an ellipse about its major axis.
Prolate Spheroid
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Elongated along the polar diameter.
Prolate
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A spheroid generated by rotating an ellipse about its minor axis,
Oblate Spheroid
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Flattened at the poles.
Oblate
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The branch of geometry that deals with solid figures and three-dimensional space.
Solid Geometry
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A solid generated by the revolution of a semicircle about its diameter, whose surface is at all points equidistant from the center.
Sphere
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A solid bounded by two parallel planes and a surface generated by a straight line moving parallel to a fixed straight line and intersecting a closed plane curve in one of the planes.
Cylinder
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A cylinder generated by a rectangle about one of its sides.
Right Circular Cylinder
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A geometric figure having the three dimensions of length, breadth, and thickness.
Solid or Body
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The extent of a three-dimensional object or the amount of space that it occupies, measured in cubic units.
Volume
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Any figure having only two dimensions, such as a plane or curved two-dimensional locus of points defining the boundary of a solid.
Surface
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An element that generates a geometric figure, esp. a straight line that generates a surface by moving in a specified fashion.
Generator or Generatrix
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A fixed line used in the description of a curve or surface.
Directrix
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A solid geometric figure bounded by plane faces.
Polyhedron
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Having all faces congruent regular polygons and all solid angles congruent.
Regular
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A polyhedrom having a polygonal base and triangular faces meeting at a common point or vertex.
Pyramid
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A regular polyhedron bounded by four plane faces.
Tetrahedron
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A solid bounded by six equal square sides, the angle between any two adjacent faces being a right angle.
Cube
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A regular polyhedron having six faces.
Hexahedron
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A polyhedron having ends that are parallel. congruent polygons and sides that are parallelograms.
Prism
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One of the five regular polyhedrons: Tetrahedron, Hexahedron, Octahedron, Dodecahedron, or Icosahedron.
Platonic Solid
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The point within a regular polygon equally distant from the vertices.
Center
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A line at which a surface terminates or at which two surfaces of a solid meet.
Edge
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A point in a geometric solid common to three or more sides.
Vertex
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A regular polyhedron having eight faces.
Octahedron
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A regular polyhedron having 20 faces.
Icosahedron
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A regular polyhedron having 12 faces.
Dodecahedron
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A solid whsoe surface is generated by a straight line, the generator, passing through a fixed point, the vertex and moving along the intersection with a closed plane curve, the directrix.
Cone
141
A cone generated by rotating a right triangle about one of its legs.
Right Circular Cone
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Having the apex, vertex, or end cut off by a plane, esp. by one parallel to the base.
Truncated
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A conic section formed by the intersection of a right circular cone with a plane that cuts through both the axis and the surface of the cone.
Ellipse
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The portion of a conical solid left after cutting off the top with a plane parallel to the base.
Frustum
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A conic section formed by the intersection of a right circular cone with a plane parallel to a generator of the cone.
Parabola
146
A plane curve formed by the intersection of a right circular cone with a plane.
Conic Section
147
A conic section formed by the intersection of a right circular cone with a plane that cuts both halves of the cone.
Hyperbola
148
