Geometry
Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and the relationships between them. It is concerned with the study of points, lines, angles, surfaces, and solids, and how they can be represented, measured, and manipulated. These relationships can be expressed in plane geometry, twodimensional figures and solid geometry, threedimensional figures. From the moment you get up in the morning geometry comes into play with everything in your environment, architecture, art, engineering, the floor you walk on, furnature, and so on.
Geometry has many practical applications in fields such as engineering, architecture, physics, and computer graphics. It is also used extensively in pure mathematics research, where it provides a foundation for other areas of mathematics. Geometry has many practical applications in fields such as architecture, engineering, and computer graphics, where it is used to design and model physical structures and objects. It is also used in fields such as physics and astronomy, where it is used to model and analyze the behavior of physical systems.
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Basic Geometrical Items
 Points
 Line segment
 Line
 Intersecting lines
 Parallel lines
 Ray
 Angle
 Curve
 Circle
 Ellipse
 Polygon
Geometry Glossary
A
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 Abscissa  The distance along the xcoordinate axis to a point on the cordinate plane.
 Acute Angle  An angle that is more than 0° but less than 90°.
 Adjacent Angle  Two angles on a plane having the same vertex and a common line.
 Adjacent Side  Next to the angle in a general triangle or next to the angle of the hypotenuse of a right triangle.
 Algorithm  A procedure used to solve a problem or a desired result.
 Altitude  The shortest distance from the base to the apex.
 Analytic Geometry (Coordinate Geometry)  The study of coordinates in a two or three dimensional space.
 Angle  Two rays sharing a common point.
 Angle Bisector  A line that divides an angle into two equal angles.
 Angle of Depression  An angle measured below a particular reference point.
 Angle of Elevation  An angle measured above a particular reference point.
 Angle Types  In order of ascending: Acute angle, Right angle, Obtuce angle, Straight angle, Reflex angle
 Antipodal Point  Two points directly opposite each other on a sphere.
 Apothem  A line segment from the center of a regular polygon to the mid point of a side.
 Arc Length  The distance along the arc or the circumference of a circle or any curve.
 Area  The inside space of a figure.
 Area Differential  The difference between an expanded or reduced area of an object.
 Arm of an Angle  Either of the two arms making up an angle.
 Ascending Order  Arranged from smallest to largest.
 Asymmetric (Asymmetrical)  Not symmetric.
 Asymptote  A line that constantly approcches a curved line but never reaches it at any distance.
 Axes  A horizontal and vertical number lines that intersect at a zero point location.
 Axiom  A statement accepted as true without proof.
 Axis  A referencr line.
 Axis of Symmetry  A line through a shape so that each side is a mirror image.
 Azimith  The direction of a line related to north.
B
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 Base  The bottom of a figure in either plane or solid geometry. If the bottom and top are parallel then either can be called base.
 Base Area  The base surface area of a solid figure.
 Bearing  An angle in degrees measured clockwise from north.
 Bisect  Divide into two congruent (equal) parts.
C
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 Cardinality  The number of objects in a set. It can either be finite set or infinite set.
 Center of a Circle  A point at a fixed equal distance from all points of the circumference of a circle.
 Center of Rotation  A point that does not move in a rotation.
 Central Angle  An angle in a circle with the vertex at the circle's center.
 Centroid  The center of a plane or mass.
 Cevian  A line or line segment that extends from a vertex of a triangle to the opposite side.
 Chord  A line segment on the interior of a circle.
 Circle  All points are at a fixed equal distance from a center point.
 Circumcenter  The point of intersection of the perpendicular bisectors of the sides.
 Circumscribed Circle (Circumcircle, Outradius)  A circle that passes through all the vertices of a twodimensional figure.
 Circumscribed (Outside)  A circle that touches every vertex.
 Circumscribed Geometry  The study of algorithms in terms of geometry.
 Circumscribed Sphere  A polyhedron is a sphere that contains the polyhedron and touches each of the ployhedron's vertices.
 Circumference  The outside of a circle or a complete circular arc.
 Collinear  When three or more points lie on a straight line.
 Collinear Points  Points that lie on the same line.
 Complememt of an Angle  Acute angle A (25°) + B = 90°. Complement of 25° is 65°.
 Complememtary Angle  Angles that add up to 90°.
 Composite Figure  One figure made up from two or more geometric figures.
 Compute  To figure out or evaluate.
 Concave  An internal angle is greater than 180°.
 Concentric  Like geometric figures that share a common center.
 Conclusion  The then... part of a conditional statement to be proved.
 Concurrent  Lines or curves that all intersect at a single point.
 Conditional Statement  An if... then... statement.
 Cone  A threedimensional figure having one circular base tapering to an apex.
 Congruent  All sides having the same lengths and angles measure the same.
 Congruent Lines  Line segments having the same length but not necessarily the same angle.
 Conjecture  A statement that might be true, but is not proven.
 Conjugate Angle  Angles that add up to 360°.
 Conic Section  A section on any plane through a circle, ellipse, hyperbola, and parabola.
 Converse  A conditional statement (if... then...) made be switched with parts of another statement.
 Convex  No internal angle is greater than 180°.
 Coordinate  Any point on a plane.
 Coordinate Plane  A plane having a horizontal and vertical axis number line intersecting at the origin.
 Coplanar  Lines and points lying on the same plane.
 Coplanar Points  Points that lying on the same plane.
 Corollary  A theroem that follows on from another theroem.
 Cross Section  A threedimensional solid figure that is intersected by a plane creating a twodimensional figure.
 Cylinder  A threedimensional figure having two circular parallel congruent bases.
D
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 Degree  When an angle goes all the way around a circle it is divided equal to 360 degrees.
 Descending Order  Arranged from largest to smallest.
 Differential  Deals with smooth curvy objects and their properties.
 Diagonal  A line from one vertices to another that is non adjacent.
 Diameter  The distance across the center of a circle.
 Directrix  The path followed by a point or line when moving.

Distance Between Two Points  Using two given coordinate points.
E
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 Edge  A line where two or more vertices come together.
 Elastic Section Modulus (S)  A single parameter that measures a crosssection's strength in bending.
 Ellipse  A twodimensional figure with a conic section or a stretched circle.
 Ellipsoid  A threedimensional figure sphere like surface for which all cross sections are ellipses.
 Empty set  A set with no objects.
 Equilateral  All the sides of a polygon are the same length.
 Euclidean Geometry  The study of plane and solid figures.
 Euclid's Postulates  Euclid's five postulates are basic rules that govern geometric figures.
 Euler line  The centroid, circumcenter, and orthocenter of any triangle always lies on a straight line.
 Euler's Constant  Also called Euler Number, is a mathematical constant.
 Expression  Any combination of numbers and variables used to create a mathematical expression or formula.
 Exterior Angle  An angle on the exterior of two rays of a plane figure.
F
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 Face  Any flat surface of a solid figure.
 Foci  Two fixed points on the interior of an ellipse used to define the curve.
 Focus  The points that construct a conic section.
 Full Angle  An angle that measures 360°.
G
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 Geodesic  The shortest distance between two points of a line segment on a sphere or other curved surface.
 Geometric Figure  Any set of points on a plane or in space (arc, circle, line, plane figure, point, solid figure, etc.).
 Geometric Properties  Characteristics of geometric figures supported by these statements: definations, postulates, theorems, and corollaries.
 Generatrix  A point or line when moved along a certain path creates a new shape.
 Geometry Postulate  A postulate is a statement that is assumed true without proof.
 Geometry Theorem  A theorem is a true statement that can be proven.
 Golden Angle  The smaller of two angles created by sectioning the circumference of a circle according to the golder ratio.
 Golden Ratio (Divine Porportion, Golden Mean, Golden Section)  A mathematical ratio commonly found in nature and design. \(\large{ \varphi=1 : 1.6180339887... }\)
 Golden Rectangle  A rectangle that can be divided into a square and a rectangle that is similar to the original rectangle.
 Great Circle  The intersection of a sphere and a plane that contains the center of the sphere.
H
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 Hexahedron  Any polyhedron with six faces.
 Horizontal  Parallel to a flat or level surface of the earth.
 Horizontal Line  A line extending left or right but not up or down.
 Hyporenuse  The side of right triangle opposite the right angle, which is the longest side.
 Hypothesis  A tentative statement that might be true. Identify the problem, research the problem, then make a proposed solution to the problem.
 Pythagorean Theorem  The hypotenuse is the sum of the squares of the other two sides in a right triangle.
I
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 Incenter  The point where the angle bisectors meet for a regular polygon or triangle.
 Incircle  A circle that touches all lines of a figure.
 Initial Side of an Angle  The inside of a ray of an xaxis of an angle.
 Inradius  The radius of a inscribed circle.
 Inscribed (Inside)  A sphere that touches the center of every faces.
 Inscribed Angle  An angle inside a circle with its vertex in the circle.
 Inscribed Circle  The largest circle possible that can fit on the inside of a twodimensional figure.
 Inscribed Sphere (Insphere)  A convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.
 Inside Angle  An angle on the interior of two rays of a plane figure.
 Interior Angle  An angle on the interior of two rays of a plane figure.
 Intersecting Lines  Lines that have only point in common.
 Interval  The region or space between two defined values.
 Inverse Statement  Disaliow both the hypohesis and conclusion of the origional statement.
 Isometric  A representation of a threedimensional figure where all three sides can be seen.
L
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 Lateral Surface Area (Lateral Surface)  The surface area of a solid figure excluding the area bases of the solid figure, just the sides.
 Line  A straight path connecting two points.
 Line Segment (Segment)  All points bertween two points.
 Line Segment Bisector  A line or line segment that cuts another line segment into two equal parts.
 Linear Pair  An interior angle combined with an exterior angle sharing the same side.
 Locus  A set of points that form a geometric figure or graph.
 Long Diagonal  Always crosses the center point of the figure.
M
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 Major Arc  The longest of two arcs of a circle or ellipse.
 Major Axis  The longest axis of a circle or ellipse.
 Mean  Another word for average.
 Median  The middle number in a data set.
 Median of a Trapezoid  A line segment from the midpoint of the legs of a trapezoid.
 Median of a Triangle  A line segment from a vertex (corner point) to the midpoint of the opposite side.
 Menelaus's Theorem  The way two cevians of a triangle divide each other and two of the triangle's sides.
 Midpoint  A point on a line segment that divides the segment into two congruent segments.
 Midsphere  A polyhedron is a sphere that is tangent to every edge of the polyhedron.
 Minor Arc  The shorter of two arcs of a circle or ellipse.
 Minor Axis  Always the shortest axis of a circle or ellipse.
 Mixed Number  A number written as a whole number and a fraction.
N
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 Noncollinear  Points that do not all lie on the same line.
 Noncollinear Points  Points that do not all lie on the same line.
 Noncoplanar Points  Points that do not all lie on the same plane.
 Nonpolyhedron  Has a solid with curved edges or sides.
 Normal  In math it means to be at right angles.
O
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 Oblique  Tilted at an angle, not horizontal or vertical.
 Oblique Cone  A threedimensional figure with the apex not alligned above the center at 90° to the base.
 Oblique Cylinder  A threedimensional figure with both bases not alligned above each other and the center not at 90° to the other base center.
 Oblique Line  A line not horizontal or vertical.
 Oblique Prism  A threedimensional figure with both bases not alligned above each other and the center not at 90° to the other base center.
 Oblique Pyramid  A threedimensional figure with the apex not alligned above the center at 90° to the base.
 Obtuse Angle  An angle that is more than 90° but less than 180°.
 Opposite Angle (Vertical Angle)  The opposite angles when two lines intersect.
 Opposite Leg  The leg of a right triangles opposite from the reference angle.
 Ordinate  The distance along the ycoordinate axis to a point on the cordinate plane.
 Origin  The intersection point (0, 0) of horizontal and vertical number lines.
 Outlier  A data point in a data set that is far outside of an established pattern.
P
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 Parallel Lines  Two lines that do not intersect.
 Parallel Planes  Two planes that do not intersect.
 Perimeter  The sum of the lengths of all sides of a plane figure.
 Perpendicular  An angle that measures 90°.
 Perpendicular Bisector  A line perpendicular to a segment passing through the segment's midpoint.
 Pi  \(\large{ \pi=3.1415926535 ... }\)
 Plane  An infinate expanse of points in two directions.
 Plane Geometry  A two dimensional figure, also called planar geometry, with edges. The edges are line segments or edges and curve segments or arcs, all lying on a flat plane.
 Plastic Section Modulus (Z)  Used to determine the limit state of a structural beam defined as the point when the entire crosssection has yielded.
 Platonic Solid  A threedimensional figure where each face is a regular polygon. There are five, cube, dodecahedron, icosahedron, octahedron, and tetrahedron.
 Point  A single location or the intersection of two lines.
 Polygon  A closed plane figure for which all edges are line segments and not necessarly congruent.
 Polyhedron  A threedimensional figure that is a solid with no curved edges or sides.
 Proportional  Having a constant ratio.
 Precision  The level of detail in a number or estimate.
 Prism  A threedimensional figure with two parallel ends that are exactly the same.
 Pyramid  A threedimensional figure that is a polyhedron with a polygonal base and lateral faces that taper to an apex.
 Pythagorean Theorem  The hypotenuse is the sum of the squares of the other two sides in a right triangle.
Q
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 Quadrilateral  A polygon with four sides.
 Quadrants  Four sections divided by the x and y axis on the xy plane. Quadrant I is the upper right, Quadrant II is the upper left, Quadrant III is the lower left, and Quadrant IV is the lower right,
 Quotient  The answer after dividing one number or expression by another.
R
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 Radian  There are 360 degrees in a circle and 2 \(\pi\) radians in a circle.
 Radical  A square root.
 Radius  A line segment between the center point and a point on a circle or sphere.
 Range  The difference between the largest and smallest nunbers in a data set.
 Ray  A line starting at a point and extending infinitely in one direction.
 Rectangular Angle  Two rectangles with different lengths that intersect at a 90° angle at one end each.
 Reference Angle  The smallest angle that the terminal side of a given angle makes with the xaxes.
 Reflection of a Line Section  Every point on a line segment appears an equal distance on the other side of a line.
 Reflex Angle  An angle that is more than 180° but less than 360°.
 Right Angle  An angle that is 90°.
S
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 Sagitta  The perpendicular from the midpoint of the arc's chord to the arc itself.
 Scale Factor  The ratio of any two corresponding lengths in two similar geometric figures.
 Scalene  If no two sides have the same length.
 Secant Line  A line that passes through at least two points on a curve.
 Section Modulus  Geometric properties for a given crosssection used in design of beams or flexable members.
 Sector of a Circle  A sector is a fraction of the area of a circle with a radius on each side and an arc.
 Segment (Line Segment)  All points bertween two points.
 Segment of a Circle  An interior part of a circle bound by a chord and an arc.
 Semimajor Axis  Half of the longest axis of a circle or ellipse.
 Semiminor Axis  Half of the shortest axis of a circle or ellipse.
 Semicircle  Half of a circle.
 Semiperimeter  One half of the perimeter.
 Set  A defined group of objects.
 Side  Any line segment of an figure.
 Similar  Identical in shape, but not necessarily the same size.
 Skew Lines  Lines that are not in the same plane and do not intersect.
 Skewed Data  Not symmetric around the mean and the data (graph) has a long tail on one or the other.
 Short Diagonal  Does not cross the center point of the figure.
 Solid  A three dimensional figure with height, width, and depth.
 Solid Geometry  A threedimensional figure with connecting edges on multiple planes. The surface of each twodimensional plane is called a face.
 Straight Angle  An angle that is 180° or pi radians.
 Standard Position of an Angle  An angle where its vertex is located at the origin and one ray is on the positive xaxis. One side of the angle is always fixed along the positive xaxis.
 Subtend  To be opposite to and extend from one side to the other of a hypotenuse.
 Supplement of an Angle  Any angle A between 0° and 180°. A is 180°  A
 Supplementary Angles  Two angles that sum to 180°.
 Surface  A threedimensional figure excluding internal points.
 Surface Area  The total area of all the surfaces of a three dimensional figure, bottom, top, and sides.
 Symmetric (Aymmetrical)  When two or more parts are congruent or identical to each other.
T
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 Tangent  A line that touches a curve at just one point such that it is perpendicular to a radius line of the curve.
 Terminal Side of an Angle  The inside of a ray of an angle oposite the xaxis initial side.
 Tessellation  A pattern made of identical shapes.
 Tetrahedron  Known as triangular pyramid.
 Threedimensional  A figure with height, width, and depth.
 Threedimensional Coordinates  A system for locating points in three dimension (height, width, and depth) using x, y, z coordinates.
 Triangulation  By observing the direction and or distance to an object from two or more observation points, the position of an object can be located.
 Translation  Moving a shape to a new location with no other changes.
 Transversal  A line that intersects at least two or more lines.
 Triangle Exterior Angle Theorm  An exteroir angle is equal to the sum of the opposite interior angles.
 Triangle Inequality Theorem  Any side of a triangle is always shorter than the sum of the other two sides.
 Triangle Inequality Theorem Converse  A triangle cannot be constructed from three line segments if any of them is longer than the sum of the other two.
 Twodimensional  A flat figure on a single plane represented by 0, 0.
V
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 Variable  A symbol used to represent a number that we do not know yet.
 Vector  A quantity with both magnitude and direction.
 Vertex  A point where two or more curves, edges, or lines meet.
 Vertical  Perpendicular to horizontal or straight up or down.
 Vertical Angle (Opposite Angle)  The opposite angles when two lines intersect.
 Vertical Line  A line at a right angle to the horizon.
 Vertices  Plural of vertex.
 Volume  The amount of space in an solid figure.
X
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 xaxis  A horizontal number line on a grid on a twodimensional plane.
 xcoordinate  The first element \(\large{ x }\) in an ordered set \(\large{ \left( x, y \right) }\) on a twodimensional plane.
Y
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 yaxis  A vertical number line on a grid on a twodimensional plane.
 ycoordinate  The second element \(\large{ y }\) in an ordered set \(\large{ \left( x, y \right) }\) on a twodimensional plane.
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 zaxis  You could say depth number line on a grid on a threedimensional plane.
 zcoordinate  The third element \(\large{ z }\) in an ordered set \(\large{ \left( x, y, z \right) }\) on a threedimensional plane.