1. **Problem Statement:** Given three quadrilaterals with markings, determine which classifications (Quadrilateral, Parallelogram, Rectangle) must be true for each figure. 2. **Key Definitions and Properties:** - A **Quadrilateral** is any four-sided polygon. - A **Parallelogram** is a quadrilateral with both pairs of opposite sides parallel. - A **Rectangle** is a parallelogram with four right angles. 3. **Figure Analysis:** **Top-left figure (A-B-C-D):** - Opposite sides have matching arrow markings, indicating they are parallel. - Diagonals have matching tick marks, indicating they bisect each other. - By definition, this confirms it is a parallelogram. - Since all parallelograms are quadrilaterals, it is also a quadrilateral. **Center figure (W-Y-X-V):** - Two top angles are congruent. - Bottom-left angle is congruent to top-right angle. - There is a right angle at vertex X. - These angle properties confirm all angles are right angles. - Therefore, it is a rectangle. - Since rectangles are parallelograms and parallelograms are quadrilaterals, it is all three. **Top-right figure (R-S-U-T):** - Right-angle marks at vertices R and T (two adjacent right angles). - Two adjacent right angles in a parallelogram imply all angles are right angles. - Therefore, it is a rectangle. - Hence, it is also a parallelogram and quadrilateral. 4. **Summary of Classifications:** - Top-left: Quadrilateral, Parallelogram - Center: Quadrilateral, Parallelogram, Rectangle - Top-right: Quadrilateral, Parallelogram, Rectangle