Question

if \\(wxyz\\) is a square, which statements must be true? check all that apply.

a. \\(\overline{wx}\\) is parallel to \\(\overline{yz}\\).
b. \\(wxyz\\) is a trapezoid.
c. \\(\overline{wx}\\) is perpendicular to \\(\overline{xy}\\).
d. \\(wxyz\\) is a rhombus.
e. \\(\angle w\\) is congruent to \\(\angle x\\).
f. \\(\angle w\\) is supplementary to \\(\angle x\\).

Explanation:

Analyze square properties

A square \(WXYZ\) is a regular quadrilateral.
It has four congruent sides and four right angles.
Thus, \(m\angle W = m\angle X = m\angle Y = m\angle Z = 90^\circ\).

Evaluate parallel and perpendicular statements

Opposite sides of a square are parallel.
Therefore, \(\overline{WX}\) is parallel to \(\overline{YZ}\).
Consecutive sides of a square are perpendicular.
Therefore, \(\overline{WX}\) is perpendicular to \(\overline{XY}\).

Evaluate quadrilateral classifications

A square is a special type of rhombus.
A rhombus is a quadrilateral with four congruent sides.
Under the inclusive definition, a trapezoid has at least one pair of parallel sides.
Since a square has parallel opposite sides, it is also a trapezoid.

Evaluate angle relationships

Using the Supplementary Angles knowledge point:
Since \(m\angle W = 90^\circ\) and \(m\angle X = 90^\circ\):
They are congruent: \(\angle W \cong \angle X\).
Their sum is \(180^\circ\), so they are supplementary.

Answer:

• A. \(\overline{WX}\) is parallel to \(\overline{YZ}\). (Correct answer)
• B. \(WXYZ\) is a trapezoid. (Correct answer)
• C. \(\overline{WX}\) is perpendicular to \(\overline{XY}\). (Correct answer)
• D. \(WXYZ\) is a rhombus. (Correct answer)
• E. \(\angle W\) is congruent to \(\angle X\). (Correct answer)
• F. \(\angle W\) is supplementary to \(\angle X\). (Correct answer)