A four-sided polygon with four congruent sides and four equal angles is a square
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That would be called a regular polygon, one with congruent(equal) side legnths and congruent angles.
It is simply a polygon with all equal angles. It is not a regular polygon - if that is what you are looking for.
Yes and providing that its interior angles are congruent as well because whilst a square is a regular polygon a rhombus is not a regular polygon although it has 4 equal sides its interior angles are not congruent.
with all sides equal (congruent) AND all angles equal (congruent). In these circumstnces the adjective "convex" is redundant.
A regular polygon has all of its sides of equal length and all of its angles congruent.