question 13 of 25

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

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

Question

question 13 of 25

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Definition", "Quadrilateral Hierarchy", "Rhombus Properties" ], "new_concepts": [], "current_concepts": [ "Square Definition", "Quadrilateral Hierarchy", "Rhombus Properties" ] } ## Analyze the properties of square WXYZ $$ \begin{aligned} &\text{Square } WXYZ \implies \text{Four right angles: } m\angle W = m\angle X = m\angle Y = m\angle Z = 90^\circ\ &\text{Square } WXYZ \implies \text{Four congruent sides: } WX = XY = YZ = ZW\ &\text{Square } WXYZ \implies \text{Opposite sides are parallel: } \overline{WX} \parallel \overline{YZ}, \quad \overline{XY} \parallel \overline{ZW} \end{aligned} $$ ## Evaluate each statement $$ \begin{aligned} &\text{A. } \overline{WX} \perp \overline{XY} \implies \text{True (consecutive sides of a square meet at } 90^\circ\text{)}\ &\text{B. } WXYZ \text{ is a rhombus} \implies \text{True (all squares have four congruent sides, making them rhombuses)}\ &\text{C. } \overline{WX} \parallel \overline{YZ} \implies \text{True (opposite sides of a square are parallel)}\ &\text{D. } \angle W \cong \angle X \implies \text{True (both are right angles, } 90^\circ = 90^\circ\text{)}\ &\text{E. } WXYZ \text{ is a trapezoid} \implies \text{False (a trapezoid has exactly/at least one pair of parallel sides, but a square is classified as a parallelogram)}\ &\text{F. } \angle W \text{ is supplementary to } \angle X \implies \text{True (} m\angle W + m\angle X = 90^\circ + 90^\circ = 180^\circ\text{)} \end{aligned} $$

A. $\overline{WX}$ is perpendicular to $\overline{XY}$.

B. $WXYZ$ is a rhombus.

C. $\overline{WX}$ is parallel to $\overline{YZ}$.

D. $\angle W$ is congruent to $\angle X$.

E. $WXYZ$ is a trapezoid.

F. $\angle W$ is supplementary to $\angle X$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Square Definition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the properties of square WXYZ

Evaluate each statement

Answer: