# Geometry Topics

2D
Having both width and length, but no thickness.
3D
Having length, width, and thickness i.e. space.
Acute Angle
A positive angle that is less than 90 degrees.
Acute Triangle
A triangle in which all of the angles are less than 90 degrees.
Two angles are adjacent if they share a common vertex and have a common side between them.
Alternate Exterior Angles
Exterior angles on alternate sides of the transversal ie not on the same parallel line.
Alternate Interior Angles
Interior angles on alternate sides of the transversal ie not on the same parallel line.
Altitude of a Trapezoid
The distance between the bases of a trapeziod.
Altitude of a Triangle
The perpendicular segment from a vertex to the line containing the opposite side of a triangle.
Angle Bisector
A ray that divides an angle into two congruent angles.
Angle of Depression
The angle in a vertical plan between the local horizontal and a descending line.
Angles
The inclination of one line to another.
Annular
Pertaining to an annulus or ring; ring shaped.
Arc
Part of a circle.
Axis of Rotation
Centre line about which rotation occurs.
Axis of Symmetry
A line that passes through a graph or figure such that one side of the figure is an exact mirror image of the other.
Ball
A sphere together with its interior.
Biconic Geometry
Two cone structure configuration.
Bijection
A one-to-one onto transformation.
Catenary
A chain suspended from two points forms this curve.
Central Angle
Angle whose vertex is placed at the center of a circle.
Cevian
A line segment extending from a vertex of a triangle to the opposite side.
Chord
A line segment that connects two points of a curve or circle.
Circle
The set of points equidistant from a given point.
Circular Cone
A cone whose base is a circle.
Circumcentre
The circumcentre of a triangle is the center of the circumscribed circle.
Circumcircle
The circle circumscribed about a figure.
Circumference
The perimeter of a circle.
Cissoid
A curve with equation y2(a-x)=x3.
Complementary Angles
Two angles whose sum is 90°.
Concentric Circles
Circles that have the same center and varying radii.
Cone
A three-dimensional solid that rises to a single point at the top. A type of light-sensitive cell in the retina.
Congruent
Equilateral, equal, exactly the same size and shape.
Congruent Angles
Two angles that are exactly the same.
Congruent Figures
Two geometric figures that are identical in size and shape.
Consecutive Sides
Sides of a polygon that share an endpoint.
Corresponding Angles
Two angles in the same relative position on two lines when those lines are cut by a transversal.
Coterminal Angles
Two angles that have the same terminal side.
Cube
A solid figure bounded by 6 congruent squares.
Cyclic Polygon
A polygon whose vertices lie on a circle.
Decagon
A polygon with ten sides.
Degree
A unit describing a plane angle, 1 degree = 1/90 right angle.
Diagonal
In a polygon, the line segment joining a vertex with another (non-adjacent) vertex is called a diagonal.
Diameter
The longest chord of a figure. In a circle, a diameter is a chord that passes through the centre of the circle.
Dihedral Angle
The angle formed by two planes meeting in space.
Dodecagon
A polygon with 12 sides.
Dodecahedron
A solid figure with 12 faces.
Domino
Two congruent squares joined along an edge.
Ellipsoid
A solid figure whose equation is x2/a2+y2/b2+z2/c2=1.
Enneagon
A nine-sided polygon.
Equiangular Polygon
A polygon all of whose interior angles are equal.
Equichordal Point
A point inside a closed convex curve in the plane is called an equichordal point if all chords through that point have the same length.
Equilateral Polygon
A polygon all of whose sides are equal.
Equilateral Triangle
A triangle with three equal sides.
Escribed Circle
An escribed circle of a triangle is a circle tangent to one side of the triangle and to the extensions of the other sides.
Euler Line
The Euler line of a triangle is the line connecting the centroid and the circumcentre.
Excentre
The centre of an excircle.
Excircle
An escribed circle of a triangle.
The radius of an escribed circle.
Face Angle
The plane angle formed by adjacent edges of a polygonal angle in space.
Fermat′s Spiral
A parabolic spiral.
Focal Chord
A chord of a conic that passes through a focus.
A line segment from the focus of an ellipse to a point on the perimeter of the ellipse.
Foot of Altitude
The intersection of an altitude of a triangle with the base to which it is drawn.
Foot of Line
The point of intersection of a line with a line or plane.
Frustum
For a given solid figure, a related figure formed by two parallel planes meeting the given solid. For a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base.
Geometric Position
True position.
Geometry Books
Lists all Books in the Encyclopaedia
Geometry Calculations
Lists all Calculations in the Encyclopaedia
Geometry Conversions
Lists all Conversions in the Encyclopaedia
Lists all Weblinks in the Encyclopaedia
Gergonne Point
In a triangle, the lines from the vertices to the points of contact of the opposite sides with the inscribed circle meet in a point called the Gergonne point.
Great Circle
A circle on the surface of a sphere whose centre is the centre of the sphere.
Half Line
A ray.
Half Plane
The part of a plane that lies on one side of a given line.
Harmonic Division
A line segment is divided harmonically by two points when it is divided externally and internally into the same ratio.
Helical
Having the shape of a helix, or screw.
Helix
A path formed as a point advances uniformly around a cylinder, as the thread on a screw or the flutes on a drill.
Hemisphere
Half of a sphere.
A 17 sided polygon.
Heptagon
A polygon with 7 sides.
Heronian Triangle
A triangle with integer sides and integer area.
A 16 sided polygon.
Hexagon
A polygon with 6 sides.
Hexagonal Prism
A prism with a hexagonal base.
Hexahedron
A polyhedron having 6 faces.
Hexomino
A polygon in the plane made of 6 equal-sized squares connected edge-to-edge.
Icosahedron
A 20 sided solid.
Incentre
The incentre of a triangle is the center of its inscribed circle.
Incircle
The circle inscribed in a given figure.
Included Angle
The angle made by two sides of a polygon.
Included Side
The side between two angles in a polygon.
Initial Side
The side that the measurement of an angle starts from.
Inscribed Angle
The angle formed by two chords of a curve that meet at the same point on the curve.
Inscribed Polygon
A polygon whose vertices lie on a circle.
Interior of a Circle
The set of points whose distance from the center of the circle is less than that of the radius.
Isogonal Conjugate
Isogonal lines of a triangle are cevians that are symmetric with respect to the angle bisector. Two points are isogonal conjugates if the corresponding lines to the vertices are isogonal.
Isosceles Tetrahedron
A tetrahedron in which each pair of opposite sides have the same length.
Isosceles Triangle
A triangle with two equal sides.
Isotomic Conjugate
Two points on the side of a triangle are isotomic if they are equidistant from the midpoint of that side. Two points inside a triangle are isotomic conjugates if the corresponding cevians through these points meet the opposite sides in isotomic points.
Kite
Knot
A curve in space formed by interlacing a piece of string and then joining the ends together.
Latus Rectum
A chord of an ellipse passing through a focus and perpendicular to the major axis of the ellipse.
Line Symmetry
If a figure is divided by a line and both divisions are mirrors of each other, the figure has line symmetry.
Loxodrome
On a sphere, a curve that cuts all parallels under the same angle.
L-tetromino
A tetromino in the shape of the letter L.
Malfatti Circles
Three equal circles that are mutually tangent and each tangent to two sides of a given triangle.
Medial Triangle
The triangle whose vertices are the midpoints of the sides of a given triangle.
Midpoint
The point M is the midpoint of line segment AB if AM=MB. That is, M is halfway between A and B.
Molecular Geometry
Shape of a molecule, based on the relative positions of the atoms.
Nagel Point
In a triangle, the lines from the vertices to the points of contact of the opposite sides with the excircles to those sides meet in a point called the Nagel point.
Nine Point Centre
In a triangle, the circumcenter of the medial triangle is called the nine point centre.
Nine Point Circle
In a triangle, the circle that passes through the midpoints of the sides is called the nine point circle.
Nonagon
A nine sided polygon.
Normal
A line perpendicular to a surface or curve.
Oblique Angle
An angle that is not a right angle.
Oblique Triangle
A triangle that is not a right triangle.
Obtuse Angle
An angle larger than 90° but smaller than 180°.
Obtuse Triangle
A triangle that contains an obtuse angle.
An 18 sided polygon.
Octagon
A polygon with 8 sides.
Octahedron
A polyhedron with 8 faces.
One Dimensional
Having length, but no width e.g. a line.
Orthic Triangle
The triangle whose vertices are the feet of the altitudes of a given triangle.
Outside Diameter
A dimension commonly used to specify the size of a cylindrical bar or pipe.
Parallel
Two or more lines are said to be parallel if they are in the same plane, but never intersect. Two or more planes are parallel if the planes never intersect.
Parallelogram of Forces
A method of resolving two forces acting on an object. This is also a great way of visualising the forces and hence resultant.
Pedal Triangle
The pedal triangle of a point P with respect to a triangle ABC is the triangle whose vertices are the feet of the perpendiculars dropped from P to the sides of triangle ABC.
A 15 sided polygon.
Pentagon
A polygon with five sides.
Pentomino
A five-square polyomino.
Perfect Cube
An integer is a perfect cube if it is of the form m3 where m is an integer.
Pivot Point
The point around which something turns.
Plane Angle
The plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius is 1 radian.
Polygon
A shape of multiple sides. Regular polygons have sides of equal length.
Polyomino
A planar figure consisting of congruent squares joined edge-to-edge.
Primitive Pythagorean Triangle
A right triangle whose sides are relatively prime integers.
Pythagorean Triangle
A right triangle whose sides are integers.
A four-sided polygon.
A prism whose base is a quadrilateral.
A pyramid whose base is a quadrilateral.
The quadrature of a geometric figure is the determination of its area.
A 14 sided polygon.
The locus of points of equal power with respect to two circle.
The radical centre of three circles is the common point of interesection of the radical axes of each pair of circles.
In a circle, the radius is the distance from the centre of the circle to a point on the circle.
Rectangle
A quadrilateral with 4 right angles.
Reflex Angle
An angle between 180° and 360°.
Regular Polygon
A polygon in which all of the angles and all of the sides are equal.
Right Angle
right angle = π/2 radians = 90°
Right Triangle
A triangle that contains a right angle.
Rotate
To rotate an object in a tessellation means to repeat the object by spinning it on a point a certain angle.
Rotation
Motion of an object where the path of every point is a circle or circular arc.
Rusty Compass
A pair of compasses that are fixed open in a given position.
Same Side Exterior Angles
Angles located outside a set of parallel lines and on the same side of the transversal.
Same Side Interior Angles
Angles located inside a set of parallel lines and on the same side of the transversal.
Scalene Triangle
A triangle in which no two sides are of equal length.
Septagon
A seven-sided polygon.
Similar Figures
Two geometric figures are similar if their sides are in proportion and all their angles are the same.
Small Circle
The circle formed by the intersection of a sphere and a plane that doesn't contain the centre of the sphere.
Solid Geometry
The study of figures in three-dimensional space.
Sphere
Basic calculations of the properties of a sphere.
Spherical Triangles
A triangle on the surface of a unit sphere.
Square
A number raised to the power 2 ie 2 x 2 = 22 = 4. Also, a 2 dimensional figure with the height and width having the same lengths,and at right angles to each other.
Square Surface
A surface at a right angle with another surface.
Straight Angle
An angle whose measure is 180 degrees.
Straightedge
As it sounds, an unmarked tool used to draw straight lines.
Supplementary Angles
Two angles are supplementary if they add up to 180°.
Surface Contour
The outline or profile of a surface.
Symmedian
Reflection of a median of a triangle about the corresponding angle bisector.
Symmetry
A figure has symmetry if it has parts that correspond with each other in terms of size, form, and arrangement.
Tangential
Having the characteristics of a tangent - a straight line touching a circle at one point and forming a right angle with the radius connecting this point with the center of the circle.
Terminal Side
The side that the measurement of an angle ends at.
Tesselation
A covering of a plane with congruent copies of the same region with no holes or overlaps.
Tetragon
A four-sided polygon.
Tetrahedron
A polyhedron with four faces.
Tetromino
A four-square polyomino.
Three Dimensional
Having length, width, and thickness i.e. space.
Toroidal
Having the specific geometrical shape of a torus.
Torus
A geometric solid in the shape of a doughnut.
Translation
Movement in a straight line without rotation.
Trapezium
A quadrilateral in which no sides are parallel.
Trapezoid
A quadrilateral that has at least one pair of parallel sides.
Triangle
A three sided shape.
Triclinic
Having three axes of any length with none of the included angles being equal to one another or 90 degrees.
Tridecagon
A 13 sided polygon.
Trigon
A three-sided polygon - a triangle.
Tromino
A three-square polyomino.
Truncated Pyramid
A section of a pyramid between its base and a plane parallel to the base.
Two Dimensional
Having both width and length, but no thickness.
Undecagon
An eleven sided polygon.
Unit Circle
Unit Cube
A cube with edge length 1.
Unit Square
A square of side length 1.
Vertical Angles
Two angles that share a common vertex and whose sides form 2 lines.
Witch of Agnesi
A curve whose equation is x2y=4a2(2a-y).
X-pentomino
A pentomino in the shape of the letter X.
Zero Angle
An angle whose measure is 0.
Zero Dimensional
Having no dimension; a point.

Subjects: Mathematics