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Perpendicular Bisectors: The diagonals of a square are perpendicular bisectors of each other, meaning they intersect at right angles, and they divide each other into two equal parts.
In the construction described earlier:
Since the square is inscribed in a circle, its diagonals (lines connecting opposite vertices) are also diameters of the circle.
By construction, the diagonals intersect at the center of the circle, which is equidistant from all points on the circumference.
Thus, the diagonals intersect at right angles, forming four congruent right triangles.
Additionally, since the square is symmetric about its diagonals, each diagonal bisects the opposite side into two equal parts
1 answer
The diagonals of a square intersect at right angles and divide each other into two equal parts, making them perpendicular bisectors. In the construction discussed previously, the diagonals of the square also serve as diameters of the circle in which the square is inscribed. The intersection point of the diagonals is the center of the circle, equidistant from all points on the circumference. Consequently, the diagonals create four congruent right triangles and bisect the opposite sides of the square into two equal parts due to the symmetry of the square about its diagonals.