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Q: What is a shape that has congruent sides and angles called?

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Angles and sides are congruent when they are identical. A shape with four identical sides and angles is a square.

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 regular polygon

none exist.

Square, rhombus possibly a parallelogram

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).

Convex polygons with congruent sides and congruent angles are called regular polygons.

That is a mathematical impossibility. At least 2 angles have to be congruent in order for the shape to have 4 sides.

Congruent Figures has equal sides, angles, shape and size.

rectangle

A polygon with 2n sides (n>1) can have opposite angles congruent.

obtuse

An octagon.

Rhombus.

trapezoid

A circle, ellipse, some irregular polygons,

Any rectangle that is not square.

A square

It is called the mystery triangle

A shape with 4 right angles and 4 equal sides is a square. ==========================

A square, because congruent means equal.

Regular polygons have congruent sides and angles

A square

It is a square

rhombus