Question

given: quadrilateral \\(wxyz\\) with \\(\overline{wx} \parallel \overline{yz}\\) and \\(\overline{wx} \cong \overline{yz}\\).

which term best describes quadrilateral \\(wxyz\\)?

• rectangle
• rhombus
• parallelogram
• trapezoid

Explanation:

Identify given geometric conditions

$$ \overline{WX} \parallel \overline{YZ} \quad \text{and} \quad \overline{WX} \cong \overline{YZ} $$

Apply the opposite sides parallel and congruent theorem

$$ \text{One pair of opposite sides is both parallel and congruent} \implies WXYZ \text{ is a parallelogram} $$

Evaluate the given multiple-choice options

$$ \text{rectangle (requires right angles), rhombus (requires equilateral sides), trapezoid (only one pair of parallel sides)} $$

Answer:

• rectangle
• rhombus
• parallelogram (Correct answer)
• trapezoid