Sum of angles of a triangleIn a Euclidean space, the sum of angles of a triangle equals a straight angle (180 degrees, πradians, two right angles, or a half-turn). A triangle has three angles, and has one at each vertex, bounded by a pair of adjacent sides. The sum can be computed directly using the definition of angle based on the dot product and trigonometric identities, or more quickly by reducing to the two-dimensional case and using Euler's identity.
PolygonIn geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself.
Line segmentPart of a straight line that is bounded by two distinct end points The geometric definition of a closed line segment: the intersection of all points at or to the right of A with all points at or to the left of B Historical image of 1699 - creating a line segment In geometry, a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the line that is between its endpoints.
Point (geometry)Fundamental object of geometry A finite set of points (in red) in the Euclidean plane. In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces. As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist.
Vertex (geometry)In geometry, a vertex (pl.: vertices or vertexes), also called a corner, is a point where two or more curves, lines, or line segmentsmeet or intersect. For example, the point where two lines meet to form an angle and the point where edges of polygons and polyhedra meet are vertices. The term vertex is also used for a different type of point in geometry, a vertex of a curve, meaning a point of extreme curvature.
GeometryBranch of mathematics Three-dimensional Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period vte Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
ShapeA shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type. In geometry, shape excludes information about the object's position, size, orientation and chirality. A figure is a representation including both shape and size (as in, e.g., figure of the Earth).
Edge (geometry)In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.
Base (geometry)In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure. This term is commonly applied in plane geometry to triangles, parallelograms, trapezoids, and in solid geometry to cylinders, cones, pyramids, parallelepipeds, prisms, and frustums.Internal and external anglesIn geometry, an angle of a polygon is formed by two adjacent sides. For a simple polygon (non-self-intersecting), regardless of whether it is convex or non-convex, this angle is called an internal angle (or interior angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex. If every internal angle of a simple polygon is less than a straight angle (πradians or 180°), then the polygon is called convex.
AngleIn geometry, an angle is formed by two lines that meet at a point. Each line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and their size or magnitude as associated quantity. Angular measure or measure of angle are sometimes used to distinguish between the measure of the quantity and figure itself.
Euclidean planes in three-dimensional spaceIn Euclidean geometry, a plane is a flat two-dimensionalsurface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional spaceR3{\displaystyle \mathbb {R} ^{3}}. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimally thin.
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