Question
Which statement proves that parallelogram `PQRT` is a rectangle?
Answers
GPT-4o mini
To prove that a parallelogram \( PQRT \) is a rectangle, you can use one of the following statements:
1. **Diagonals are equal**: If the diagonals of the parallelogram are equal in length, then it is a rectangle.
2. **Right angles**: If at least one angle in the parallelogram is a right angle (90 degrees), then all angles are right angles, making it a rectangle.
3. **Congruent adjacent angles**: If we can show that two adjacent angles are congruent, it implies that each angle of the parallelogram must be a right angle due to the properties of the angles in a parallelogram.
4. **Sides are perpendicular**: If one pair of adjacent sides in the parallelogram are perpendicular to each other, then the parallelogram is a rectangle.
You can utilize any of these statements to demonstrate that parallelogram \( PQRT \) is a rectangle.
1. **Diagonals are equal**: If the diagonals of the parallelogram are equal in length, then it is a rectangle.
2. **Right angles**: If at least one angle in the parallelogram is a right angle (90 degrees), then all angles are right angles, making it a rectangle.
3. **Congruent adjacent angles**: If we can show that two adjacent angles are congruent, it implies that each angle of the parallelogram must be a right angle due to the properties of the angles in a parallelogram.
4. **Sides are perpendicular**: If one pair of adjacent sides in the parallelogram are perpendicular to each other, then the parallelogram is a rectangle.
You can utilize any of these statements to demonstrate that parallelogram \( PQRT \) is a rectangle.