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What quadrilateral has both pairs of opposite sides congruent?
A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
What is a quadrilateral with two pairs of congruent adjacent sides congruent and no congruent opposite sides?
Diamond
Two pairs of parallel sides and all angles congruent?
Two different quadrilaterals have two pairs of parallel sides and have all their angles congruent. They are the square and the rectangle.
What shape has 2 pairs of congruent sides with those sides being non-adjacent and the angles are not all congruent?
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).
Which quadrilaterals have both pairs of opposite sides that are congruent?
A parallelogram if the two pairs are mutually congruent but all four sides are not. A rhombus if all four are.
