Question

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

Answer 1

Answer: A. WXYZ is a parallelogram

B.
`\angle{W}` is a right angle.

D.
`\overline{WX}\cong\overline{XY}`

E.
`\angle{W}\cong\angle{Y}`

F.
`\angle{W}` is supplementary to
`\angle{Y}`.

Explanation:

Given: WXYZ is a square.

A. A square is a parallelogram because its opposite sides are equal.

B.
`\angle{W}` is a right angle , since all the interior angles in a square area right angle.

C. A trapezoid has two equal parallel sides and two non-parallel sides.

But square has opposite sides parallel , therefore WXYZ is not a trapezoid.

D. Since all the sides of a square are congruent to each other , therefore

`\overline{WX}\cong\overline{XY}`

E. Since all the angles of a square are congruent to each other , therefore

`\angle{W}\cong\angle{Y}`

F. Since , all the interior angles in a square area right angle.

Thus,
`\angle{W}+\angle{Y}=90^(\circ)+90^(\circ)=180^(\circ)`

Hence,
`\angle{W}` is supplementary to
`\angle{Y}`.

Answer 2

True statements are,

A, B, D, E , and F

Explanation:

Properties of a square

1) All sides are equal

2) All angles are equal to 90°

3) Opposite sides are parallel

A. WXYZ is a parallelogram

True (property 3)

B. <W is right angle

True (Property 2)

C. WXYZ is a trapezoid

False

D. WX ≅ XY

True (Property 1)

E. <W congruent to <Y

True (Property 1)

F. <W is supplementary to <Y

True (Property 2)

True statements are,

A, B, D, E , and F