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No, but a regular pentagon is equilateral. Equilateral means that all sides are congruent (equal in measure); to be regular, all angles also have to be congruent.
Equilateral just means equal sided. An equilateral pentagon is therefore a pentagon with all its sides of equal length. If an equilateral pentagon is also an equal-angled pentagon then it is called a regular pentagon.
convex, equiangular, equilateral, regular. APEX****
Yes, by definition. If it not equilateral AND equiangular, then it is not regular.
Squares, rhombera, and equilateral triangles are always regular.