# 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.
**Adjacent Angles**- 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 y
^{2}(a-x)=x^{3}. **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 x
^{2}/a^{2}+y^{2}/b^{2}+z^{2}/c^{2}=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.
**Exradius**- 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.
**Focal Radius**- 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
**Geometry Weblinks**- 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.
**Heptadecagon**- A 17 sided polygon.
**Heptagon**- A polygon with 7 sides.
**Heronian Triangle**- A triangle with integer sides and integer area.
**Hexadecagon**- 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**- A quadrilateral which has two pairs of adjacent sides equal.
**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.
**Octadecagon**- 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.
**Pentadecagon**- 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 m
^{3}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.
**Quadrangle**- A four-sided polygon.
**Quadrangular Prism**- A prism whose base is a quadrilateral.
**Quadrangular Pyramid**- A pyramid whose base is a quadrilateral.
**Quadrature**- The quadrature of a geometric figure is the determination of its area.
**Quadridecagon**- A 14 sided polygon.
**Radical Axis**- The locus of points of equal power with respect to two circle.
**Radical Centre**- The radical centre of three circles is the common point of interesection of the radical axes of each pair of circles.
**Radius**- 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 = 2
^{2}= 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**- A circle with radius 1.
**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 x
^{2}y=4a^{2}(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