Q

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.

Views

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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