QQuestionMathematics
QuestionMathematics
# Question 10 of 25
Multiple Response: Please select all correct answers and click "submit."
If WXYZ is a square, which statements must be true? Check all that apply.
$\square$ A. WXYZ is a parallelogram.
$\square$ B. $\angle W$ is a right angle.
$\square$ C. WXYZ is a trapezoid.
$\square$ D. $W X \cong X Y$
$\square$ E. $\angle W$ is congruent to $\angle Y$.
$\square$ F. $\angle W$ is supplementary to $\angle Y$.
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Answer
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Step 1:: A square is a special type of rectangle where all sides are equal in length.
$\square$ A.
Hence, it is a parallelogram since opposite sides of a parallelogram are equal. WXYZ is a parallelogram. (This statement is true.)
Step 2:: In a square, not only are opposite sides equal, but all sides are equal.
$\square$ B. $\angle W$ is a right angle. (This statement is true.)
Step 3:: A square is also a special type of trapezoid where the two parallel sides are equal in length.
$\square$ C.
However, not all trapezoids have this property. WXYZ is a trapezoid. (This statement is true.)
Step 4:: In a square, since all sides are equal, two consecutive sides are also equal.
$\square$ D. $W X \cong X Y$. (This statement is true.)
Step 5:: In a square, since all angles are right angles, consecutive angles are congruent.
$\square$ E. $\angle W$ is congruent to $\angle Y$. (This statement is true.)
Step 6:: In a square, since all angles are right angles, consecutive angles do not supplement each other.
$\square$ F. $\angle W$ is supplementary to $\angle Y$. (This statement is false.)
Final Answer
The true statements are A, B, C, D, and E.
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