There are infinitely many possible shapes. For example an octagon with sides [sequentially] numbered 1 and 5 that are equal.
Another ViewYes the above is true, but specifically a shape with twopairs of congruent, opposite sides is called a parallelogram.
A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
A quadrilateral with both pairs of opposite sides congruent is a parallelogram.
Diamond
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).
2 pairs, the sides opposite each other are congruent to each other
A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
a parallelogram.
A quadrilateral with both pairs of opposite sides congruent is a parallelogram.
Diamond
Trapezoid.
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).
rectangle
2 pairs, the sides opposite each other are congruent to each other
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * both pairs of opposite angles are congruent * one pair of opposite sides are parallel and congruent * both diagonals bisect each other * all consecutive angle pairs are supplementary
This shape would be a square.
No, it doesn't have to be. A quadrilateral can definitely be a parallelogram only if: - Both pairs of opposite sides are parallel. - Both pairs of opposite sides are congruent. - One pair of opposite sides are both congruent and parallel. - Both pairs of opposite angles are congruent. - The diagonals bisect each other.
A kite