Subjects geometry

Rectangle Parallelogram E22E5D

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

Use the AI math solver

1. The problem is to select the correct rephrased statement that Vera can use to prove that any rectangle is also a parallelogram. 2. Recall the definitions: - A rectangle is a quadrilateral with four right angles ($90\degree$). - A parallelogram is a quadrilateral where opposite sides are parallel. 3. To prove a rectangle is a parallelogram, we need to show that opposite sides are parallel. 4. Statement A says: If opposite sides are parallel, then all angles are $90\degree$. This is true for rectangles but is a conditional in the wrong direction for the proof. 5. Statement B says: If all angles are $90\degree$, then opposite sides are parallel. This matches the definition of a rectangle implying it is a parallelogram. 6. Statement C involves congruent sides implying right angles, which is not generally true. 7. Statement D says: If all angles are $90\degree$, then opposite sides are congruent. While true for rectangles, this does not directly prove parallelism. 8. Therefore, the correct rephrased statement for Vera's proof is Statement B. **Final answer:** B