Final answer:
To prove a parallelogram with one right angle is a rectangle, we look at the parallelogram's properties: opposite equal angles and supplementary adjacent angles. This necessitates that all angles in such a parallelogram are right angles, confirming it is a rectangle.
Step-by-step explanation:
To prove that a parallelogram with at least one right angle is a rectangle, we must use the properties of a parallelogram and the definition of a rectangle. A parallelogram is a quadrilateral with opposite sides that are equal and parallel. A rectangle is defined as a parallelogram with four right angles.
Since a parallelogram has opposite angles that are equal, if one angle is a right angle, the opposite angle must also be a right angle. Additionally, adjacent angles in a parallelogram are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 90 degrees, its adjacent angle must also be 90 degrees to fulfill the supplementary requirement. Consequently, all angles in the parallelogram must be right angles, satisfying the definition of a rectangle.
This logical sequence establishes that if a parallelogram has at least one right angle, then all angles must be right angles, thereby proving it to be a rectangle.