Question

In a square $PQ$ $RS$, diagonals bisect sach other at $O$. Prove that
$\Delta POQ\cong \Delta QOR\cong \Delta ROS\cong \Delta SOP$

Answer 1

In $△POQ$ & $△QOP$

$PO=OR$ [bisect]

$OQ=OQ$ [Common]

$\angle POQ=\angle ROQ$

[diagonal bisect each other at ${90}^o$]

$△POQ\cong △QOP\left[SAS\right]$

Similarly $△POS\cong △SOR$

$△SOR\cong △QOR$

$△QOP\cong △POS$

from all these

$△POR\cong △QOR\cong △ROS\cong SOP$