Possibly but not necessarily.
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yes.
yes. it does
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You can do that by simply proving that the hexagon is a regular hexagon. You could do this by dividing the hexagon into 6 equilateral triangles of the same size successfully that tesselate to form a hexagon, thus proving that all sides are equal.
Irregular hexagon has 2 right angles all other sides are congruent. How large is each one?