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The only shape that always has equal sides and equal angles is the square.
Other shapes can have equal sides and angles (like a triangle or octagon), but they are not by definition equilateral.
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I think it is worth noting that any regular polygon satisfies the definition. Conversely, as you point out, you have to explicitly specify that it is regular.
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What is a ten sided geometrical figure called?
A decagon - if the sides are all equal, and the angles are all equal, it is a regular decagon.
A four-sided figure with 4 equal sides and no right angles?
A four-sided polygon with all sides equal and no right angles would be a rhombus. A rhombus consists of two acute angles and to obtuse angles.
A rectangle with 4 right angles and all sides the same length?
Such a figure is called a square. Actually only one right angle is enough to force the the other angles to be right, and if three sides are equal, that forces all sides in such a figure to be equal. Exercise: Prove that any 4-sided figure( called a quadrilateral in math books) with three equal sides and one right angle is a square.
What does regular and irregular mean?
A regular polygon (a closed plane figure of straight lines) has all equal angles and all equal side lengths. For example, a square is a regular quadrilateral, because it's four edges are all the same length, and it's angles are all equal (90 degrees). A regular triangle is an equilateral triangle.An irregular polygon does not have equal sides and angles. N.B to be regular, a polygon must have both equal sides and equal angles. If a polygon has equal sides but unequal angles it is not a regular polygon.
What is a regular shape?
A shape where all the sides are equal and all the angles are equal. If all sides are equal but angles or not, it is equilateral. If it is vice versa, it is equiangular.
