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If WXYZ is a square, which statements must be true? Check all that apply.

AWX is perpendicular to XY.
BW is congruent to X.
CW is supplementary to X.
DWXYZ is a rhombus.
EWXYZ is a trapezoid.

F. WX is parallel to YZ.

Verified Answer :

Answer:

The correct options are A, B, C, D and F.

Step-by-step explanation:

It is given that WXYZ is a square.

All four sides of square are equal and the measure all interior angles of square are equal, i.e, 90 degree.

Two consecutive sides are perpendicular to each other therefore

\(WX\perp XY\)

Option A is correct.

All interiors angles of a square are congruent therefore

\(W\cong X\)

Option B is correct.

Sum of two consecutive angles of a square is always 180 degree, therefore two consecutive angles are supplementary angles.

\(\angle W+\angle X=90^{\circ}+90^{\circ}=180^{\circ}\)

Option C is correct.

Since all sides are equal and the opposite angles of square are same, therefore square is a special case of rhombus.

Option D is correct.

In a trapezoid only one pair of opposite sides is parallel, but in a square both pairs of opposite sides are parallel. Therefore a trapezoid can not be a square.

Option E is incorrect.

Opposite sides of square are parallel to each other, therefore

\(WX\parallel YX\)

Option F is correct.

WX is perpendicular to XY, W is congruent to X, W is supplementary to X, WXYZ is a rhombus, and WX is parallel to YZ and this can be determined by using the properties of a square.

Given :

WXYZ is square.

The properties of a square are given below:

  • All sides are equal in length.
  • The two consecutive sides are perpendicular.
  • Opposite sides are parallel to each other.
  • All the interior angles are 90 degrees.
  • The diagonals bisect one another.
  • The area of the square whose sides are 'a' is \(\rm a^2\).
  • The perimeter of the square whose sides are 'a' is 4a.
  • DIagonal are equal.

Therefore, the correct statements about the square WXYZ are A), B), C), D), and F).

For more information, refer to the link given below:

https://brainly.com/question/17241228

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