Question

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.

Answer 1

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.

Answer 2

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