A. A parallelogram is a rectangle if and only if its diagonals are congruent.
B. A parallelogram is a rhombus if and only if its diagonals are congruent.
C. A quadrilateral is a square if and only if it is a rhombus and a rectangle.
D. A quadrilateral is a rectangle if and only if it has four right angles.
The statement that is false is choice A. On a parallelogram, the diagonals will always be congruent even if it is not a rectangle. To test this, draw numerous parallelograms and draw in the diagonals. They will be the same length even though they are not rectangles.
