QQuestionMathematics
QuestionMathematics
If WXYZ is a square, which statements must be true? Check all that apply.
A. WX is perpendicular to XY.
B. W is congruent to X.
C. W is supplementary to X.
D. WXYZ is a rhombus.
E. WXYZ is a trapezoid.
F. WX is parallel to YZ.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the properties of a square
A square is a special quadrilateral with the following unique characteristics: - All four sides are equal in length - All four angles are right angles (90 degrees) - Opposite sides are parallel - Diagonals are equal in length and bisect each other
Step 3:: Analyze each statement systematically
- $$\therefore$$ This statement is TRUE
A. WX is perpendicular to XY - In a square, ALL adjacent sides are perpendicular to each other B. W is congruent to X - In a square, all vertices are congruent (equal in size and shape) C. W is supplementary to X - Supplementary angles sum to 180 degrees - In a square, adjacent angles are 90 degrees, not supplementary D. WXYZ is a rhombus - A rhombus has all sides equal - A square IS a special type of rhombus E. WXYZ is a trapezoid - A trapezoid has only one pair of parallel sides - A square has TWO pairs of parallel sides F. WX is parallel to YZ - In a square, opposite sides are always parallel
Final Answer
The true statements are A, B, D, and F.
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