Final answer:
The diagonals of a rhombus are perpendicular and bisect each other, but they are not always congruent. They can only be congruent if the rhombus is also a square, which is a special case. Therefore, the correct option is (c) Never congruent, except in the special case of a square.
Step-by-step explanation:
In geometry, a rhombus is a type of polygon known as a quadrilateral. It has four sides of equal length and its opposite sides are parallel. An important property of a rhombus is that its diagonals bisect each other at right angles. However, the diagonals of a rhombus are not always congruent; rather, they are usually of different lengths. One diagonal is the line segment joining two opposite acute angles, and the other diagonal is the line segment joining two opposite obtuse angles. The length of the diagonals is dependent on the size of the angles, but because the angles are not equal (except in a square, which is a special type of rhombus), the diagonals are generally not equal either.
To illustrate this, consider a rhombus with sides of equal length 'a'. If the diagonals were congruent, they would divide the rhombus into four congruent right triangles. But since the angles of a rhombus are not equal (except in a square), the triangles formed are not congruent, and thus the diagonals are not congruent. In summary, the diagonals of a rhombus are perpendicular to each other and bisect each other, but they are not always congruent. They can only be congruent if all angles are right angles, in which case the rhombus is also a square.
Therefore, the answer to the question "Are the diagonals of a rhombus always congruent?" is (c) Never congruent, except in the special case of a square, which is both a rectangle and a rhombus with congruent diagonals.