Question

fill in the blank. the diagonals of a rhombus are ______.
a. perpendicular and do not necessarily bisect each other
b. parallel
c. perpendicular and bisect each other
d. sometimes equal

Explanation:

To solve this, we recall the properties of a rhombus. A rhombus is a parallelogram with all sides equal. The diagonals of a rhombus have two key properties: they are perpendicular to each other (intersect at 90 degrees) and they bisect each other (divide each other into two equal parts). Let's analyze each option:

• Option A: Diagonals of a rhombus do bisect each other, so this is incorrect.
• Option B: Diagonals of a rhombus are not parallel; they intersect, so this is incorrect.
• Option C: This matches the properties of a rhombus's diagonals (perpendicular and bisect each other), so this is correct.
• Option D: While the diagonals of a rhombus can be equal (when it's a square, a special case of a rhombus), the main defining property of a rhombus's diagonals is being perpendicular and bisecting each other, not "sometimes equal" as a primary property. So this is not the best answer.

Answer:

C. perpendicular and bisect each other