Question: prove by vector method if the diagonals of a parallelogram are equal then it is a rectangle?
Answer: Yes if diagonals of a parallelogram are equal then it is a rectangle. Let PQRS be a parallelogram. To show that PQRS is a rectangle, we have to prove that one of its interior angles is 90º. Since PQRS is a parallelogram and one of its interior angles is 90º, PQRS is a rectangle.