1. **Problem Statement:** Determine which conclusions must be true for a quadrilateral that has a line of symmetry. 2. **Understanding the Problem:** A line of symmetry in a quadrilateral means the figure can be folded along that line so that the two halves match exactly. 3. **Key Properties of Symmetric Quadrilaterals:** - The line of symmetry divides the quadrilateral into two mirror-image halves. - Corresponding parts on either side of the line are congruent. 4. **Analyzing Each Conclusion:** - "All sides of the quadrilateral have the same length." This is not necessarily true. For example, an isosceles trapezoid has a line of symmetry but not all sides are equal. - "All angles of the quadrilateral have the same measure." This is not necessarily true. Symmetry does not imply all angles are equal. - "Two sides of the quadrilateral have the same length." This must be true because the line of symmetry pairs sides on either side, making at least one pair congruent. - "Two angles of the quadrilateral have the same measure." This must be true for the same reason as sides; angles on either side of the line of symmetry are congruent. - "No sides of the quadrilateral have the same length." This contradicts the property of symmetry. - "No angles of the quadrilateral have the same measure." This also contradicts the property of symmetry. 5. **Final Answer:** The conclusions that must be true are: - Two sides of the quadrilateral have the same length. - Two angles of the quadrilateral have the same measure.