Let-a-1-a-2-a-n-be-the-side-lengths-of-an-equiangular-polygon-Prove-that-if-a-1-a-2-a-n-then-the-polygon-is-regular-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 16735 by Tinkutara last updated on 26/Jun/17

Let a_1 , a_2 , ..., a_n be the side lengths of an equiangular polygon. Prove that if a_1 ≥ a_2 ≥ ... ≥ a_n , then the polygon is regular.

$$\mathrm{Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:…,\:{a}_{{n}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{side}\:\mathrm{lengths}\:\mathrm{of}\: \\ $$$$\mathrm{an}\:\mathrm{equiangular}\:\mathrm{polygon}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{if} \\ $$$${a}_{\mathrm{1}} \:\geqslant\:{a}_{\mathrm{2}} \:\geqslant\:…\:\geqslant\:{a}_{{n}} ,\:\mathrm{then}\:\mathrm{the}\:\mathrm{polygon}\:\mathrm{is} \\ $$$$\mathrm{regular}. \\ $$

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Let-a-1-a-2-a-n-be-the-side-lengths-of-an-equiangular-polygon-Prove-that-if-a-1-a-2-a-n-then-the-polygon-is-regular-

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