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Geometry Definitions

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Browse our growing collection of geometry definitions:

AAS Congruence

AAS Congruence or angle angle side congruence is when two triangles have corresponding angles and sides that are congruent as shown in the image below, the triangles are congruent.

AA Similarity

AA Similarity or angle angle similarity means when two triangles have corresponding angles that are congruent as shown in the image below, the triangles are similar.

Abscissa

In mathematics, the abscissa and the ordinate are respectively the first and second coordinates of a point in a coordinate system. The abscissa is the first coordinate in an ordered pair and the ordinate is the second coordinate.

Accuracy

Accuracy is how close an approximation is to an actual value. In other terms, in measurement of a set, accuracy refers to closeness of the measurements to a specific value, while precision refers to the closeness of the measurements to each other.

Acute Angle

An acute angle is an angle that has a measure less than π2 radians or 90° degrees.

Acute Triangle

An acute triangle (or acute angled triangle) is a triangle in which all three interior angles are acute angles (less than π2 radians or 90 degrees).

Altitude

Altitude otherwise referred to as height is defined based on the context in which it is used (aviation, geometry, geographical survey, sport, atmospheric pressure, and many more). For mathematics altitude is 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.

Altitude of a Cone

The altitude or height of a cone is the distance from the apex of a cone to its base. It is the shortest line segment between the apex of a cone and the (possibly extended) base. Altitude can also be used to refer to the specific length of this segment.

Altitude of a Cylinder

The altitude or height of a cylinder is the distance between the bases of a cylinder. It is the shortest line segment between the (possibly extended) bases. Altitude can also be used to refer to the specific length of this segment.

Altitude of a Parallelogram

The altitude or height of a parallelogram is the distance between opposite sides of a parallelogram. It is the shortest line segment between opposite sides. Altitude can also be used to refer to the specific length of this segment.

Altitude of a Prism

The altitude or height of a prism is the distance between the two bases of a prism. It is the shortest line segment between the (possibly extended) bases. Altitude can also be used to refer to the specific length of this segment.

Altitude of a Pyramid

The altitude or height of a pyramid is the distance from the apex to the base of a pyramid. It is the shortest line segment between the apex of a pyramid and the (possibly extended) base.

Altitude of a Trapezoid

The altitude or height of a trapezoid is the distance between the two bases of a trapezoid. It is the shortest line segment between the bases. Altitude can also be used to refer to the specific length of this segment.

Altitude of a Triangle

The altitude or height of a triangle is the distance between a vertex of a triangle and the opposite side. It is the shortest line segment between a vertex of a triangle and the (possibly extended) opposite side.

Annulus

A annulus or washer is the region between two concentric circles which have different radii. The area of a annulus = π (R2 − r2)

Apex

An apex is the vertex of an isosceles triangle having an angle different from the two equal angles. An apex can also be the common vertex at the top of a figure like a pyramid or of a cone.

Area of a Circle

The area of a circle is calculated using the formula: A = πr2 where r represents the circles radius.

Area of an Equilateral Triangle

The area of an equilateral triangle is calculated using the formula: A = s2 3 4 where s represents the equilateral triangles common side length.

Bidimensional Space

Bidimensional space otherwise referred to as two dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (a point).

Chord

A chord of a circle is a straight line segment on the interior of a circle whose endpoints both lie on that circle. The infinite line extension of a chord is a secant line, or just secant.

Circumference

Circumference may be defined by some as the distance around the outside of an arbitrary closed object (sometimes restricted to a closed curved object).

Collinear

In geometry, collinearity of a set of points is the property of their lying on a single line. A set of points with this property is said to be collinear (sometimes spelled as colinear).

Compression

A compression or contraction is a transformation in which a figure grows smaller. Compressions may be with respect to a point (compression of a geometric figure) or with respect to the axis of a graph (compression of a graph).

Concurrent

Concurrent refers to when two or more lines or curves all intersect at a single point.

Diameter

Diameter is a line segment connecting two points on a circle or sphere which pass through the center. Diameter is also used to refer to the specific length of this line segment.

Endecagon

A endecagon otherwise referred to as a undecagon, hendecagon or 11-gon in geometry is an eleven sided polygon.

Equidistant

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

Fixed

Fixed means that the object is regarded as fixed in the plane so that it may not be picked up and flipped if referring to a planar object. As a result, mirror images are not necessarily equivalent for fixed objects.

Height

Height otherwise referred to as altitude is defined based on the context in which it is used (aviation, geometry, geographical survey, sport, atmospheric pressure, and many more). For mathematics height is 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.

Height of a Cone

The height or altitude of a cone is the distance from the apex of a cone to its base. It is the shortest line segment between the apex of a cone and the (possibly extended) base. Height can also be used to refer to the specific length of this segment.

Height of a Cylinder

The height or altitude of a cylinder is the distance between the bases of a cylinder. It is the shortest line segment between the (possibly extended) bases. Height can also be used to refer to the specific length of this segment.

Height of a Parallelogram

The height or altitude of a parallelogram is the distance between opposite sides of a parallelogram. It is the shortest line segment between opposite sides. Height can also be used to refer to the specific length of this segment.

Height of a Prism

The height or altitude of a prism is the distance between the two bases of a prism. It is the shortest line segment between the (possibly extended) bases. Height can also be used to refer to the specific length of this segment.

Height of a Pyramid

The height or altitude of a pyramid is the distance from the apex to the base of a pyramid. It is the shortest line segment between the apex of a pyramid and the (possibly extended) base.

Height of a Trapezoid

The height or altitude of a trapezoid is the distance between the two bases of a trapezoid. It is the shortest line segment between the bases. Height can also be used to refer to the specific length of this segment.

Height of a Triangle

The height or altitude of a triangle is the distance between a vertex of a triangle and the opposite side. It is the shortest line segment between a vertex of a triangle and the (possibly extended) opposite side.

Hendecagon

A hendecagon otherwise referred to as a undecagon, endecagon or 11-gon in geometry is an eleven sided polygon. The name hendecagon, from Greek hendeka which means eleven and gon meaning corner, is often preferred to the hybrid undecagon, whose first part is formed from Latin term undecim for eleven.

Horizontal

Horizontal means oriented in a position perpendicular to up and down, and therefore parallel to a flat surface. For instance, a floor or the horizon are both horizontal.

Kite

A kite is a planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b that are congruent.

Obtuse Angle

An obtuse angle is an angle that has a measure greater than π2 radians or 90° degrees but less than π radians or 180° degrees.

Obtuse Triangle

An obtuse triangle (or obtuse angled triangle) is a triangle in which one of the interior angles is an obtuse angle (greater than π2 radians or 90 degrees but less than π radians or 180 degrees).

Ordinate

In mathematics, the ordinate and abscissa are respectively the second and first coordinates of a point in a coordinate system. The ordinate is the second coordinate in an ordered pair and the abscissa is the first coordinate.

Pappus\'s Theorem

Pappus\'s theorem or the theorem of Pappus generally refer to several different theorems. They include Pappus\'s centroid theorem, the Pappus chain, Pappus\'s harmonic theorem, and Pappus\'s hexagon theorem.

Perimeter

A perimeter is a path that encompasses or surrounds a two-dimensional shape. The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary.

Pi (Π, π)

Pi (Π, π) is the sixteenth letter of the Greek alphabet, representing the sound [p]. In the system of Greek numerals it has a value of 80.

Similar

Two figures are said to be similar when all corresponding angles are equal and all distances are increased or decreased in the same ratio, called the ratio of magnification.

Takeout Angle

A takeout angle is the angle cut out of a circular surface or piece of paper so that the surface can be rolled into a right circular cone.

Tau (Τ, τ)

Tau (Τ, τ) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.

Theorem of Pappus

The theorem of Pappus or Pappus’s theorem generally refer to several different theorems. They include Pappus\'s centroid theorem, the Pappus chain, Pappus\'s harmonic theorem, and Pappus\'s hexagon theorem.

Theta (Θ, θ)

Theta (Θ, θ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth. In the system of Greek numerals it has the value 9.

Transversal

A transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two other lines in the Euclidean plane are parallel.

Truncated Cone or Pyramid

A truncated cone or pyramid is a cone or pyramid which has its apex cut off by an intersecting plane. The plane may be either oblique or parallel to the base.

Truncated Cylinder or Prism

A truncated cylinder or prism is a cylinder or prism which has one base cut off by an intersecting plane. The other base is unaffected by the truncation.

Two Dimensional

Two dimensional or two dimensions is the property of a plane that indicates that motion can take place in two perpendicular directions.

Two Dimensional Space

Two dimensional space otherwise referred to as bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (a point).

Two Dimensions

Two dimensions or two dimensional is the property of a plane that indicates that motion can take place in two perpendicular directions.

Undecagon

A undecagon otherwise referred to as a hendecagon, endecagon or 11-gon in geometry is an eleven sided polygon.

Undefined Slope

Undefined slope occurs when the slope is for a vertical line. A vertical line has an undefined slope because all points on the line have the same x-coordinate.

Unit Circle

The unit circle is a circle with a radius of 1 which is centered at the origin on the x-y plane.

Varignon Parallelogram of a Quadrilateral

A Varignon Parallelogram of a Quadrilateral is a parallelogram formed by connecting the midpoints of adjacent sides of a quadrilateral.

Vertex

A vertex is a special point of a mathematical object and is usually a location where two or more lines or edges meet. In other terms, a vertex is a corner point of a geometric figure.

Vertical

Vertical means oriented in a straight up and down position. For instance, a wall is vertical.

Vertical Angles

Vertical angles are angles that are opposite one another at the intersection of two lines. In other terms, given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles.

Vertical Hyperbola

A vertical hyperbola is a conic section that can be thought of as an inside-out ellipse that opens upwards or downwards. In more formal terms a hyperbola means for two given points, the foci, a hyperbola is the locus of points such that the difference between the distances to each focus is constant.

Volume

Volume is the total amount of space enclosed or occupied in a solid. Volume generally has units of length and distance cubed (such as cm3, in3, m3 km3, etc.)

Volume by Parallel Cross Sections

The formula (Volume = ab A(x) dx, where A(x) is the formula for the area of parallel cross-sections over the entire length of the solid.) and image below gives the volume of a solid.

Washer

A washer or annulus is the region between two concentric circles which have different radii. The area of a washer = π (R2 − r2)

Washer Method

The washer method is a method for computing the volume of a solid of revolution that is hollow about its axis by integrating over the volumes of infinitesimal washer-shaped slices bounded by planes perpendicular to the axis of revolution.

X-Intercept

A point at which a graph intersects with the x-axis. The x-intercepts of a function must be real numbers, unlike roots and zeros of a function.

X-Y Plane

A plane formed by the x-axis and the y-axis.

X-Z Plane

A plane formed by the x-axis and the z-axis.

Y-Intercept

A point at which a graph intersects the y-axis.

Y-Z Plane

A plane formed by the y-axis and the z-axis.

Zero Dimensions

Zero dimensions or zero dimensional is the property of a point that indicates no motion is possible without leaving that point. Stating a point has zero dimensions means that the only vector contained on the point is the zero vector.

Zero Slope

A slope of zero means that the line is a horizontal line. A horizontal line has slope of 0 because all of its points have the same y-coordinate.

Z-Intercept

A point at which a graph intersects the z-axis.

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