Question
Which statement proves that parallelogram PQRT is a rectangle?
P Q
▭ 8
T 15 R
P Q
▭ 8
T 15 R
Answers
Answered by
GPT-4o mini
To prove that parallelogram PQRT is a rectangle, you will need to demonstrate that at least one of the following conditions holds true:
1. **Opposite angles are equal**: In a rectangle, all angles are 90 degrees. If you can show that the angles at each vertex of PQRT are right angles, then PQRT is a rectangle.
2. **Diagonals are equal**: A rectangle has diagonals that are equal in length. If you can show that the lengths of diagonal PR and QT are equal, then PQRT is a rectangle.
3. **Adjacent sides are perpendicular**: If you can show that at least one pair of adjacent sides are perpendicular (i.e., they meet at a right angle), then PQRT can be classified as a rectangle.
4. **All sides are perpendicular** (a less commonly used property): This is another approach but typically used when other conditions fail.
In this case, you have provided some dimensions: with one side listed as 8 and another side as 15. If you clarify which sides these dimensions refer to and provide information regarding the angles or the diagonals, then it would be possible to determine if PQRT is indeed a rectangle using the criteria above.
In conclusion, you would need to show one of the conditions mentioned to conclude that PQRT is a rectangle.
1. **Opposite angles are equal**: In a rectangle, all angles are 90 degrees. If you can show that the angles at each vertex of PQRT are right angles, then PQRT is a rectangle.
2. **Diagonals are equal**: A rectangle has diagonals that are equal in length. If you can show that the lengths of diagonal PR and QT are equal, then PQRT is a rectangle.
3. **Adjacent sides are perpendicular**: If you can show that at least one pair of adjacent sides are perpendicular (i.e., they meet at a right angle), then PQRT can be classified as a rectangle.
4. **All sides are perpendicular** (a less commonly used property): This is another approach but typically used when other conditions fail.
In this case, you have provided some dimensions: with one side listed as 8 and another side as 15. If you clarify which sides these dimensions refer to and provide information regarding the angles or the diagonals, then it would be possible to determine if PQRT is indeed a rectangle using the criteria above.
In conclusion, you would need to show one of the conditions mentioned to conclude that PQRT is a rectangle.