1. **Problem Statement:** Given that \(\angle CDF\) is a right angle and \(DE \cong CD\), we need to determine which term describes segment \(DF\) among altitude, perpendicular bisector, angle bisector, or median. 2. **Key Information:** - \(\angle CDF\) is a right angle, meaning \(DF\) is perpendicular to \(CD\). - \(DE \cong CD\) means \(D\) is the midpoint of segment \(EC\) or that \(DE\) and \(CD\) are equal in length. 3. **Definitions:** - **Altitude:** A segment from a vertex perpendicular to the opposite side. - **Perpendicular bisector:** A line that is perpendicular to a segment and divides it into two equal parts. - **Angle bisector:** A line that divides an angle into two equal angles. - **Median:** A segment from a vertex to the midpoint of the opposite side. 4. **Analysis:** - Since \(\angle CDF\) is right, \(DF\) is perpendicular to \(CD\). - Since \(DE \cong CD\), point \(D\) lies such that it divides segment \(EC\) into two equal parts. - Therefore, \(DF\) is perpendicular to \(CD\) and passes through the midpoint of \(EC\). 5. **Conclusion:** - \(DF\) is the **perpendicular bisector** of segment \(EC\). **Final answer:** \(DF\) is the perpendicular bisector.