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Question

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.

Answer 1

The intersection of the diagonals in a square creates right angles, dividing each diagonal into two equal parts. This makes them perpendicular bisectors. Additionally, the diagonals also serve as diameters for the circle in which the square is inscribed. The point of intersection of the diagonals acts as the center of the circle, equidistant from all points on the circumference. As a result, the diagonals form four congruent right triangles and divide the opposite sides of the square into equal parts due to the symmetry of the square about its diagonals.