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Congruence of Diagonals: The diagonals of a square are congruent, meaning they have the same length.
In the construction described:
Both diagonals of the square are radii of the circle.
By construction, the compass is set to the radius of the circle, and the same radius is used to construct both diagonals.
Since the compass setting remains unchanged, the length of both diagonals is equal to the radius of the circle, ensuring that they are congruent.
So, based on the construction method described, we can be confident that the diagonals of the constructed square are perpendicular bisectors of each other and congruent, meeting the criteria for a square.
1 answer
The diagonals of a square are congruent, meaning they have the same length. In the construction method outlined, both diagonals of the square are created using the radius of the circle. The compass is set to the radius of the circle, ensuring that both diagonals have the same length. This construction guarantees that the diagonals of the square are perpendicular bisectors of each other, meeting the requirements for a square. Consequently, we can confidently conclude that the diagonals of the square are congruent.