Square, rhombus
possibly a parallelogram
none exist.
That is a mathematical impossibility. At least 2 angles have to be congruent in order for the shape to have 4 sides.
Convex polygons with congruent sides and congruent angles are called regular polygons.
A quadrilateral with four congruent sides and no right angles is called a rhombus. In a rhombus, all sides are equal in length, and opposite angles are equal, but the angles are not constrained to 90 degrees. The shape can appear as a slanted square or diamond.
Congruent Figures has equal sides, angles, shape and size.
square
Angles and sides are congruent when they are identical. A shape with four identical sides and angles is a square.
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
a regular polygon
none exist.
That is a mathematical impossibility. At least 2 angles have to be congruent in order for the shape to have 4 sides.
Convex polygons with congruent sides and congruent angles are called regular polygons.
A polygon that has congruent sides and congruent angles is called a Regular polygon. If the number of sides is given, you can be more specific. Some examples: 3 congruent sides/angles = equilateral triangle 4 congruent sides/angles = square 5 congruent sides/angles = regular pentagon 6 congruent sides/angles = regular hexagon ...and so on, by adding "regular" in front of the shape's name.
A quadrilateral with four congruent sides and no right angles is called a rhombus. In a rhombus, all sides are equal in length, and opposite angles are equal, but the angles are not constrained to 90 degrees. The shape can appear as a slanted square or diamond.
rectangle
A polygon with 2n sides (n>1) can have opposite angles congruent.
Congruent Figures has equal sides, angles, shape and size.