Two geometric figures are [i]equidecomposable [/i]if each can be partitioned into the same finite number of parts that are pairwise congruent.[br][br]Equidecomposability is an equivalence relation, and each class is called an [i]area[/i].[br]This means that two equidecomposable figures are equivalent, that is they have the same area.[br][br][i]Start the animation and discover a visual proof of the equidecomposability of a regular pentagon with the equivalent triangle.[/i]
Any regular polygon can be either inscribed in or circumscribed about a circle.[br][br]What can you say about the height of the triangle equivalent to a regular polygon, if you consider the circumscribed circle, rather than the inscribed one, as the reference?
Can we say the same holds for every cyclic polygon, not necessarily regular?[br]Explain your reasoning.