Q: What shape has congruent adjacent sides?

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obtuse

A square or a rhombus

A quadrilateral with congruent pairs of adjacent sides and no parallel sides is a kite.

Trapezoid.

Two pairs of adjacent sides are congruent. The angles between the non-congruent sides are congruent.

Related questions

obtuse

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).

Square

a square

a parallelogram.

A square or a rhombus

rectangle

This is a rectangle.

A quadrilateral with congruent pairs of adjacent sides and no parallel sides is a kite.

An impossibility. By definition a quadrilateral with 4 congruent sides must have congruent adjacent angles.

Diamond

Trapezoid.