These polygons are respective generalizations of isosceles trapezia and kites, and defined by the following two 'side-angle' dual results.
Dynamic hexagon examples are given below.
|Alternate sides cyclic-2n-gons||Alternate angles circum-2n-gons|
|A cyclic 2n-gon has n distinct pairs of adjacent angles equal, if and only if, a set of alternate sides are equal.||A circumscribed 2n-gon has n distinct pairs of adjacent sides equal, if and only if, a set of alternate angles are equal.|
Alternate sides cyclic-2n-gons and Alternate angles circum-2n-gons
1) In the first figure, drag vertices A, B, D or F and in the second one, drag P, Q, R or S to dynamically change the figures.
2) Drag the first figure until all the angles are equal to obtain a semi-regular angle-gon.
3) Drag the second figure until all the sides are equal to obtain a semi-regular side-gon.
Reference: De Villiers, M. (2011). Feedback: Equi-angular cyclic and equilateral circumscribed polygons. Mathematical Gazette, July, 95(533), p. 361.
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Michael de Villiers, created 2011, updated 13 July 2018.