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