8)Suppose that a given parallelogram is not a rhombus or a rectangle. 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 angles are not all congruent.
D) None of the above
I chose C according to the definitions I had, but I'm still not sure.
Agree, C
To determine the correct answer, let's analyze the properties of a parallelogram, rhombus, and rectangle.
1) Parallelogram: A parallelogram is a quadrilateral with opposite sides that are parallel. Its opposite angles are congruent, but not necessarily all angles.
2) Rhombus: A rhombus is a parallelogram in which all sides are congruent. Its opposite angles are congruent, and its diagonals are perpendicular bisectors of each other.
3) Rectangle: A rectangle is a quadrilateral with all interior angles measuring 90 degrees. It is also a parallelogram and a rhombus. The diagonals of a rectangle are congruent and bisect each other perpendicularly.
Given that the parallelogram in question is neither a rhombus nor a rectangle, we can conclude that:
C) Its angles are not all congruent.
This is because a rhombus and rectangle both have congruent angles, but since the given parallelogram is not either of these, we can infer that its angles are not all equal.