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Take a square sheet, say PQRS (Fig 3.42). Fold along both the diagonals. Are their mid-points the same? Check if the angle at O is 90° by using a set-square. This verifies the property stated above.

Take a square sheet, say PQRS (Fig 3.42). Fold along both the diagonals. Are their mid-points the same? Check if the angle at O is 90° by using a set-square. This verifies the property stated.

Property: The diagonals of a square are perpendicular bisectors of each other.

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PO = OR       ( Square is a type of parallelogram)

By SSS congruency rule,  \triangle POS  and  \triangle ROS are congruent triangles.

                                         \triangle POS\cong \triangle ROS

                                  \therefore \angle POS = \angle ROS

                                  &   \angle POS + \angle ROS = 180\degree

                                                    2\times \angle ROS = 180\degree

                                                            \angle ROS = 90\degree

Hence,\angle O = 90\degree.

Thus,we can say that the diagonals of a square are perpendicular bisectors of each other

                      

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