Yes, that's what "regular" means.
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If the hexagon's sides and angles are congruent, then it a regular hexagon.
Yes, providing that it is in the form of a regular 6 sided hexagon
Any polygon called "regular" or "equilateral" will have congruent sides and angles. An equilateral triangle, a square, and a regular hexagon are examples.
A hexagon with 6 congruent sides is a regular hexagon
Is an irregular hexagon.