Question

choose all answers that describe the polygon wxyz if \\(\overline{wx} \cong \overline{xy} \cong \overline{yz} \cong \overline{zw}\\), \\(\text{m}\angle w = \text{m}\angle y\\), and \\(\text{m}\angle x = \text{m}\angle z\\).

answer

• parallelogram
• quadrilateral
• rectangle
• rhombus
• square
• trapezoid

Explanation:

1. Quadrilateral: The polygon has 4 vertices (W, X, Y, Z), so it is a 4-sided quadrilateral by definition.
2. Parallelogram: A quadrilateral with two pairs of opposite angles equal ($m\angle W = m\angle Y$, $m\angle X = m\angle Z$) is a parallelogram.
3. Rhombus: This parallelogram has all 4 sides congruent ($\overline{WX} \cong \overline{XY} \cong \overline{YZ} \cong \overline{ZW}$), which fits the definition of a rhombus.

We cannot confirm it is a rectangle or square because there is no information stating the angles are right angles, and it does not meet the definition of a trapezoid (which has only one pair of parallel sides, unlike this figure with two pairs).

Answer:

Quadrilateral, Parallelogram, Rhombus