quadrilaterals are consecutive and opposite angles always congruent?
square
Most quadrilaterals do not.
squares
Most quadrilaterals will not have congruent diagonals: rectangles (incl squares) and isosceles trapezium are the exception.
It depends - Quadrilaterals such as Squares are regular. Others, like the rectangle or other 'wierd' or irregular shapes aern't... Since regular polygons have, by definition, congruent sides and congruent angles, the only quadrilaterals that would be regular are squares. Rectangles have 4 congruent angles, but their sides are not all congruent, so it wouldn't count. Similarly, the only regular triangles would be equilateral triangles, since they are the only ones with all sides and all angles congruent.
Assuming you have a regular hexagon, drawing a line between every other vertex and the center will give you three congruent quadrilaterals (that also happen to be parallelograms... in fact, they are rhombuses).
quadrilaterals are consecutive and opposite angles always congruent?
There is no specific name for them.
There are 16 non-congruent quadrilaterals on a 3x3 geoboard.
The answers are No and No. In the first case, a rhombus, and in the second, a rectangle are examples of quadrilaterals which satisfy the congruence requirements but neither is a regular polygon.
square
Rectangles
Not generally.
Trapezoid?
Rectangles have all angles congruent,
Most quadrilaterals do not.