Equilateral triangle or square or rhombus or regular polygon.. All depends how many sides!
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Not quite. A regular polygon also requires all angles to be the same. Once you have a polygon with more than 3 sides, they can be equilateral without being equiangular (cf square and rhombus in the above answer).
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If a parallelogram has all four sides the same length it's called a square.
it is called a isosceles shape if iT only has 2 sides that have the same exact length
It is called an isosceles traiangle.
This is called a Parallelogram. Each pair of opposite sides will then be the same length. If all four sides are the same length, and opposite sides are parallel, then it is a rhombus. NB: If all four sides are the same length then the opposite sides must be parallel.
A three-sided polygon is called a triangle. If two of the sides are of the same length, it is said to be an isosceles triangle.