Question

choose all answers that describe the quadrilateral vwxy if m\angle v = m\angle w = m\angle x = m\angle y and diagonal \overline{vx} meets diagonal \overline{wy} at a right angle. answer attempt 1 out of 2 parallelogram rectangle rhombus square trapezoid

Explanation:

• Parallelogram: In a parallelogram, opposite angles are equal (\(m\angle V = m\angle X\), \(m\angle W=m\angle Y\)), but the diagonals are not necessarily perpendicular.
• Rectangle: In a rectangle, all angles are \(90^{\circ}\) (\(m\angle V = m\angle W=m\angle X = m\angle Y = 90^{\circ}\)), and the diagonals are equal in length but not perpendicular (except in the special case of a square).
• Rhombus: In a rhombus, opposite angles are equal (\(m\angle V = m\angle X\), \(m\angle W=m\angle Y\)), and the diagonals are perpendicular bisectors of each other.
• Square: A square is a special case of a rhombus and a rectangle. It has \(m\angle V = m\angle W=m\angle X = m\angle Y = 90^{\circ}\) (opposite angles equal) and its diagonals are perpendicular bisectors of each other.
• Trapezoid: In a trapezoid (a non - parallelogram trapezoid), only one pair of sides is parallel, and there is no guarantee that \(m\angle V = m\angle W=m\angle X = m\angle Y\) and the diagonals are not perpendicular in general.

Answer:

Rhombus, Square