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.
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
rhombus
It is a rhombus
A square is a plane geometric figure having 4 equal sides and 4 right angles.
The rectangle
Rhombus!
square
A sguar.
A regular quadrilateral. A plane shape with four sides which are equal in length and which meet at right angles.