When is a rhombus a square?

1. Define a rhombus: A rhombus is a quadrilateral with all four sides equal in length. Its opposite angles are equal, and its diagonals bisect each other at right angles.
2. Define a square: A square is a quadrilateral with all four sides equal in length and all four angles equal to 90 degrees (right angles).
3. Compare rhombus and square properties:
- Both rhombuses and squares have four equal sides.
- A rhombus has opposite angles equal, while a square has all angles equal to 90 degrees.
- A rhombus's diagonals bisect each other at right angles, which is also true for a square.
4. Identify the distinguishing property: The key difference between a rhombus and a square is the measure of their angles. For a rhombus to be a square, its angles must be right angles (90 degrees).
5. Evaluate the options:
- A. When its sides are congruent: This is true for all rhombuses, so it doesn't make it a square.
- B. When its angles are right angles: This condition, along with the property of equal sides (which a rhombus already has), defines a square.
- C. When its sides are parallel: All parallelograms, including rhombuses, have parallel opposite sides. This doesn't make it a square.
- D. When its angles are convex angles: All interior angles of a convex quadrilateral are less than 180 degrees, which is true for both rhombuses and squares. This is not a distinguishing property.