Question

The diagonals of quadrilateral WXYZ intersect at R. If R is the midpoint of WY¯¯¯¯¯¯¯and XZ¯¯¯¯¯¯, which additional statement shows that WXYZ is a rectangle?

Answer 1

Answer:

m∠WXY = 90°

Step-by-step explanation:

A quadrilateral is a polygon with four sides and four angles.

A rectangle is a quadrilateral with two pairs of opposite and parallel sides. The following are properties of a rectangle:

1. Opposite sides are congruent to each other.
2. Opposite sides are parallel to one another.
3. The diagonals are equal to each other.
4. The diagonals bisect each other.
5. All the interior angles are equal to each other. Each interior angle measures 90°.

Given quadrilateral WXYZ.  R is the midpoint of WY and XZ.

This means that R is the midpoint of the diagonals WY and XZ. this shows that the diagonals bisect each other.

For quadrilateral WXYZ to be a rectangle, each interior angle must be 90°. Hence m∠WXY = 90°