not in all shapes.
A Rectangle.
You are a square
You are a square or a rectangle
a square
A shape with four sides and perpendicular diagonals is called a rhombus. In a rhombus, all sides are of equal length, and the diagonals bisect each other at right angles. Additionally, the diagonals are not necessarily of equal length, which distinguishes a rhombus from a square.
triangle
A square and a rectangle have diagonals of equal lengths
A Rectangle.
You are a square
Not normally but in the shape of an isosceles trapezium they are equal
You are a square or a rectangle
rhombus
a square
Any rectangle will have diagonals that are equal. Don't forget that since squares are also a special type of rectangle that they would also have congruent diagonals as well.
A rectangle
a pentagon
A rhombus.