Suppose that a given parallelogram is not a rhombus or a rectangle. Which of the following can
you conclude about this parallelogram?
A) It is a square.
B) Its angles are not all congruent.
C) Its diagonals are perpendicular bisectors of each other.
D) None of the above
clearly B
To answer this question, we need to understand the properties of parallelograms, rhombuses, rectangles, and squares.
A parallelogram is a quadrilateral with opposite sides that are equal in length and parallel to each other. It does not have any specific requirements for its angles.
A rhombus is a parallelogram with all sides congruent, meaning they have the same length. Its opposite angles are also congruent.
A rectangle is a parallelogram with four right angles (angles of 90 degrees). Its opposite sides are congruent.
A square is a special type of rectangle where all sides are congruent, and all angles are right angles.
Now, given that the parallelogram in the question is neither a rhombus nor a rectangle, we can eliminate options A and C.
Option A states that the parallelogram is a square, but since it has already been stated that it is not a rectangle, which is a prerequisite for being a square, we can conclude that option A is not applicable.
Option C states that the diagonals of the parallelogram are perpendicular bisectors of each other. However, this property is specific to rectangles and squares, which we have already ruled out. Hence, option C is also not applicable.
Therefore, the only conclusion we can make is option B: The angles of the parallelogram are not all congruent. This is because there are no specific requirements for the angles in a parallelogram, and the other options are specific to rectangles and squares, which have been excluded in the question.