Suppose that a given parallelogram is not a rhombus. Which of the following can you conclude about this parallelogram?
A) Its diagonals are perpendicular bisectors of each other.
B) It is a square.
C) Its sides are not all congruent.
D) All of the above
I picked C.
So did I.
To determine which of the options is true, we need to analyze each option and eliminate the incorrect ones.
A) "Its diagonals are perpendicular bisectors of each other." This option describes the properties of a rhombus, not a parallelogram in general. Since we are given that the parallelogram is not a rhombus, we can conclude that option A is not true.
B) "It is a square." A square is a specific type of parallelogram where all four sides are congruent and all angles are right angles. Since the question states that the parallelogram is not a rhombus, we cannot conclude that it is a square. Therefore, option B is not true.
C) "Its sides are not all congruent." This option describes the properties of a parallelogram in general, not specifically a rhombus or square. Since the given information states that the parallelogram is not a rhombus, we can conclude that its sides are not all congruent. Thus, option C is true.
D) "All of the above." Since options A and B are not true, we can eliminate option D as well.
Therefore, the correct answer is C) "Its sides are not all congruent."