We have to form a quadrilateral by connecting the midpoints of the square. The side of the square: a. The side of the new quadrilateral: x² = (a/2)² + (a/2)² x² = a²/4 + a²/4 = a²/2 x = a√2 / 2 All sides of the quadrilateral are equal: a√2 / 2. So it could be another square or a rhombus. But all interior angles of the new quadrilateral are the same: 90°. Answer: This is the square.
