The geometrical shape, square satisfies the conditions.
A perfect square Four 90 degree angles and four equal sides
An isosceles trapezoid will have diagonals of equal length but will never contain right angles by definition. A square and rectangle will have diagonals of equal length but will contain 4 right angles. A rhombus and any other parallelogram that does not contain right angles will not have diagonals of equal length.
A quadrilateral that has no right angles and has four sides of equal length is a rhombus. In a rhombus, all sides are equal, but the angles are not necessarily 90 degrees. It can have acute or obtuse angles, distinguishing it from a square, which has right angles.
If you mean all right angles are equal in MEASURE, then this would be a square or a rectangle, but if you meant 4 right angles and 4 sides of equal length then that would be a square.
square
A square is a plane geometric figure having 4 equal sides and 4 right angles.
rhombus
It is a rhombus
A shape that has four sides of equal length and no right angles is called a rhombus. In a rhombus, the opposite angles are equal, and the diagonals bisect each other at right angles. Unlike a square, which is a special type of rhombus with right angles, a rhombus can have various angles that are not 90 degrees.
A regular quadrilateral. A plane shape with four sides which are equal in length and which meet at right angles.
The rectangle
square