Final answer:
To prove that if the diagonals of a quadrilateral are perpendicular and congruent, then the quadrilateral is a square, we can use the properties of squares.
Step-by-step explanation:
To prove that if the diagonals of a quadrilateral are perpendicular and congruent, then the quadrilateral is a square, we can use the properties of squares. A square is a quadrilateral with all four sides congruent and all four angles equal to 90 degrees. If the diagonals of a quadrilateral are perpendicular, it means that they form a 90 degree angle between each other. If the diagonals are also congruent, it means that they have equal lengths. Therefore, if a quadrilateral has perpendicular and congruent diagonals, it must have all the properties of a square, making it a square.