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In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star .
The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.
A tangential polygon (one that has an incircle tangent to all its sides) is equilateral if and only if the alternate angles are equal (that is, angles 1, 3, 5, ... are equal and angles 2, 4, ... are equal). Thus if the number of sides n is odd, a tangential polygon is equilateral if and only if it is regular. [1]
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
(The ordering of the sides of the blue quadrilateral is "mixed" which results in two of the interior angles and one of the diagonals not being congruent.) For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices).
An equilic quadrilateral has two opposite equal sides that when extended, meet at 60°. A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7]
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1. However, some school ...
Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [1] but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. [2] [3] A kite may also be called a dart, [4] particularly if it is ...