There are instances that quadrilateral angles can be consecutive and opposite angles are congruent. The best examples are square and rectangle.
Rectangles, of which squares are a special case.
All quadrilaterals have consecutive and opposite angles.
Consecutive angles are supplementary Diagonals bisect each other Opposite angles are congruent Opposite sides are parallel
A trapezoid
quadrilaterals are consecutive and opposite angles always congruent?
Opposite sides are parallel, Consecutive angles are supplementary, Opposite angles are congruent, Opposite sides are congruent (APEX)
rectangle and square
There are instances that quadrilateral angles can be consecutive and opposite angles are congruent. The best examples are square and rectangle.
Square and Rectangle
Rectangles, of which squares are a special case.
All quadrilaterals have consecutive and opposite angles.
Consecutive angles are supplementary Diagonals bisect each other Opposite angles are congruent Opposite sides are parallel
A trapezoid
If one angle is right, then all angles are right. The diagonals of a parallelogram bisect each other. Opposite angles are congruent. Opposite sides are congruent. Consecutive angles are supplementary.
square and a rectangle
A parallelogram (and all its special cases) has two pairs of opposite sides that are congruent. An isosceles trapezium has one pair of congruent opposite sides. Selected irregular quadrilaterals can have a pair.