Short Answer 
To prove that the parallelogram WXYZ is a rectangle, first confirm its defining properties: it must have four right angles and opposite sides equal in length. Next, verify the side lengths and angles of WXYZ, ensuring opposite sides are equal and all angles are right angles, concluding that WXYZ is indeed a rectangle based on these characteristics.
Step 1: Understand the Properties of a Rectangle
To prove that a parallelogram, specifically WXYZ, is a rectangle, you need to first understand the key properties that define a rectangle. A rectangle has the following characteristics:
- Four right angles.
- Opposite sides that are equal in length.
- Adjacent sides that are perpendicular to each other.
Establishing that WXYZ has these properties will be crucial in the proof.
Step 2: Verify Side Lengths and Angles
Next, you need to verify specific measurements and relationships within the figure WXYZ. Since it’s given that WXYZ is a parallelogram, you can use these properties:
- WZ is equal to XY (opposite sides).
- YZ is equal to WX (opposite sides).
- Angles
Showing that opposite angles are congruent and utilizing the Side-Angle-Side (SAS) property for triangles will solidify your argument.
Step 3: Conclude with Rectangular Properties
Finally, conclude your proof by summarizing the findings related to side lengths and angles. If you confirm that:
- WZ = XY and YZ = WX (from the properties of a parallelogram),
- All angles are right angles, and
- Opposite angles are congruent,
then you can definitively state that WXYZ is a rectangle based on the established properties. This comprehensive analysis supports the claim and completes the proof.