1. **Problem Statement:** Determine if the given parallelogram is a rhombus, rectangle, or square based on the properties of its diagonals. 2. **Key Properties of Parallelograms:** - A **rhombus** has all sides equal and diagonals that are perpendicular. - A **rectangle** has diagonals that are congruent (equal in length) but not necessarily perpendicular. - A **square** is both a rhombus and a rectangle, meaning it has equal sides and diagonals that are both congruent and perpendicular. 3. **Given Information:** - The parallelogram has diagonals that intersect at right angles (perpendicular). - The sides are marked equal (indicated by red "x" marks). 4. **Analysis:** - Since the diagonals are perpendicular, this suggests the parallelogram could be a rhombus or a square. - Since all sides are equal, this confirms the shape is at least a rhombus. - The right angle where diagonals intersect and equal sides imply the parallelogram is a square because it satisfies both rhombus and rectangle properties. 5. **Conclusion:** - The parallelogram is a square. 6. **Reasoning:** - The diagonals are perpendicular (property of rhombus). - The diagonals are congruent (property of rectangle). - The parallelogram has equal sides. - Therefore, it is both a rhombus and a rectangle, which defines a square. **Final answer:** The parallelogram is a square because it has equal sides and diagonals that are both perpendicular and congruent.