You have, five parallelograms. Four of the parallelograms are rectangles and one is a rhombus. Further, if the rhombus is not a square, and at least two of the rectangles are squares, which of the following choice is true?
A. No rhombus is a parallelogram.
B. Exactly one rectangle is a rhombus.
C. No rectangles are parallelograms.
D. Each parallelogram is a rectangle.
E. At least three of the parallelograms are rhombus.
The only one that is true is E: three parallelograms that are known to be rhombuses are the one designated a rhombus and the two rectangles which are known to be squares.
Originally Posted by winsome
A and C are never true: every rhombus is a parallelogram and every rectangle is a parallelogram.
B is false: at least two of the rectangles are squares, and hence are rhombuses.
D is false: the rhombus is not a square, and hence it's not a rectangle either.