Subjects geometry

Diagonals Bisect

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem:** If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral. 2. **Formula and Rules:** - A quadrilateral whose diagonals bisect each other is a parallelogram. - If the diagonals also intersect at right angles (90°), the parallelogram is a rhombus. 3. **Explanation:** - Diagonals bisecting each other means each diagonal cuts the other into two equal parts. - Right angle intersection means the diagonals are perpendicular. 4. **Conclusion:** - Therefore, the quadrilateral is a **rhombus**. This is because only in a rhombus do the diagonals bisect each other at right angles. Final answer: **Rhombus**.