Alternate sides cyclic-2n-gons and Alternate angles circum-2n-gons

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.

Back to "Dynamic Geometry Sketches"

Back to "Student Explorations"

Michael de Villiers, created 2011, updated 13 July 2018.

Alternate sides cyclic-2n-gons and Alternate angles circum-2n-gons

.sketch_canvas { border: medium solid lightgray; display: inline-block; }