If quadrilateral ABCD is a parallelogram and its adjacent angles are congruent, then the statement that must be true is:
- A) Quadrilateral ABCD is a square.
- B) Quadrilateral ABCD is a rhombus.
- C) Quadrilateral ABCD is a rectangle.
In this case, if adjacent angles are congruent, it means that each pair of angles not only share a common side but also are equal in measure. In a parallelogram, this implies that each angle would be 90 degrees. Hence, ABCD is not just a parallelogram but a rectangle because a rectangle is defined as a parallelogram with all angles being right angles.
Thus, the correct answer is:
- C) Quadrilateral ABCD is a rectangle.
To summarize, while the statement about it being a rhombus or a square could hold in some cases, the specific condition of adjacent angles being congruent leads us to conclude that ABCD must be a rectangle. A square is a specific type of rectangle where all sides are also equal, and a rhombus has equal sides but not necessarily right angles.