To answer this question, let’s analyze each option for its properties regarding quadrilaterals with congruent adjacent angles.
- a) Parallelogram: True. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (add up to 180 degrees). While not all adjacent angles are congruent, the description does fit in some specific cases (like rectangles).
- b) Rhombus: True. A rhombus is a special type of parallelogram where adjacent angles are supplementary. Again, this may not mean they are congruent, but fits under a broader category.
- c) A rectangle that is not a square: True. All angles in a rectangle are congruent, and therefore, adjacent angles in rectangles are also congruent.
- d) Square: True. A square is a type of rectangle where all sides and angles are equal, hence all adjacent angles are congruent.
- e) Isosceles trapezoid: False. In an isosceles trapezoid, the non-parallel sides are equal, and it does not necessarily mean adjacent angles are congruent.
- f) A kite that is not a rhombus: False. Kites generally have two pairs of adjacent angles that are equal, but if it’s not a rhombus, the description of being congruent for all adjacent angles doesn’t hold.
In conclusion, the correct options for a quadrilateral with adjacent angles that are congruent are: a) Parallelogram, b) Rhombus, c) A rectangle that is not a square, d) Square.