Question

the diagonals of a rhombus are ______.

a. never congruent
b. sometimes equal
c. perpendicular
d. parallel

Explanation:

Analyze properties of a rhombus

Using the Rhombus Properties knowledge point
A rhombus is defined as a parallelogram with four congruent sides.

Analyze the diagonals

Using the Diagonals of a Rhombus knowledge point
By geometric theorem, the diagonals of any rhombus bisect each other at right angles, meaning they are perpendicular.

Evaluate the given options

Using the Diagonals of a Rhombus knowledge point

• Option A: The diagonals can be congruent if the rhombus is a square, so they are not "never congruent".
• Option B: The diagonals are equal in length only when the rhombus is a square, so "sometimes equal" is true, but "perpendicular" is a fundamental defining property for all rhombuses.
• Option C: The diagonals are always perpendicular to each other.
• Option D: The diagonals intersect, so they can never be parallel.

Answer:

• A. never congruent
• B. sometimes equal
• C. perpendicular (Correct answer)
• D. parallel