1. **Problem Statement:** Identify the type(s) of quadrilateral CDEF given that all sides are equal ($CD = DE = EF = FC$) and the diagonals are equal in length ($CE = DF$). 2. **Key Properties and Formulas:** - A **parallelogram** has opposite sides equal and opposite angles equal. - A **rectangle** is a parallelogram with equal diagonals. - A **rhombus** has all sides equal but diagonals are generally not equal. - A **square** has all sides equal and equal diagonals, combining properties of a rectangle and a rhombus. 3. **Analysis:** - Since all sides are equal, CDEF is at least a rhombus. - Since the diagonals are equal, it satisfies the rectangle property. - A quadrilateral with all sides equal and equal diagonals is a square. 4. **Conclusion:** - CDEF is a **square**. - It is also a parallelogram (all squares are parallelograms). - It is a rectangle (equal diagonals and right angles implied by equal sides and diagonals). - It is a rhombus (all sides equal). **Answer:** ☑ Parallelogram ☑ Rectangle ☑ Rhombus ☑ Square