FTCE Professional Education Practice Exam

Which statement about rhombuses is true?

1. All rhombuses are parallelograms

2. No rhombuses are parallelograms

3. Some rhombuses are not parallelograms

4. Rhombuses cannot be squares

The correct answer is: All rhombuses are parallelograms

The statement that all rhombuses are parallelograms is true because a rhombus is defined as a quadrilateral with all four sides of equal length. This definition inherently satisfies the properties of a parallelogram, which requires opposite sides to be equal and parallel. Therefore, every rhombus is indeed a specific type of parallelogram. In addition, a rhombus also has the property that its opposite angles are equal and its diagonals bisect each other at right angles, further aligning it with parallelogram characteristics. Consequently, this classification is consistent across all instances of rhombuses, regardless of their other qualities, such as whether they have right angles or equal-length diagonals. The other options fail to acknowledge the relationship that exists between rhombuses and parallelograms. They inaccurately suggest either that rhombuses are completely separate from or that some can exist outside the category of parallelograms, which contradicts the fundamental definition and properties of these shapes in geometry.