Question

which of the following statements are true for a rhombus? select all that apply.a) all four sides are congruent.b) consecutive angles are supplementary.c) all four angles are congruent.d) the diagonals are congruent.e) the diagonals are perpendicular.f) the diagonals bisect each other.

Explanation:

A rhombus is a quadrilateral with specific properties:

1. All four sides are equal (congruent) by definition.
2. Consecutive angles are supplementary (sum to $180^\circ$) because it is a parallelogram.
3. Its diagonals are perpendicular to each other.
4. Rhombus angles are only congruent if it is a square (a special case, not all rhombuses), so general rhombuses do not have congruent angles.
5. Rhombus diagonals are only congruent if it is a square, so this is not true for all rhombuses.
6. The diagonals of all parallelograms (including rhombuses) bisect each other.

Answer:

A. All four sides are congruent.
B. Consecutive angles are supplementary.
E. The diagonals are perpendicular.
F. The diagonals bisect each other.