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This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
In modern terms, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [57] The size of an angle is formalized as an angular measure. In Euclidean geometry, angles are used to study polygons and triangles, as well as forming an object of study in their own right. [43]
See the figures in this article for examples. The three defining points may also identify angles in geometric figures. For example, the angle with vertex A formed by the rays AB and AC (that is, the half-lines from point A through points B and C) is denoted ∠BAC or ^. Where there is no risk of confusion, the angle may sometimes be referred to ...
A triangle in which one of the angles is a right angle is a right triangle, a triangle in which all of its angles are less than that angle is an acute triangle, and a triangle in which one of it angles is greater than that angle is an obtuse triangle. [8] These definitions date back at least to Euclid. [9]
That is, the result of moving a shape around, enlarging it, rotating it, or reflecting it in a mirror is the same shape as the original, and not a distinct shape. Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points in a closed chain, as well as the resulting interior points.
The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle.
A right circular cone and an oblique circular cone A double cone (not shown infinitely extended) 3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex that is not contained in the base.