Question

diagonals of parallelogram bisects each other prove:seg:PO=segRQ​

Answer 1

PQRS is a parallelogram where PR and QS are diagonals intersect at point O

In △POS and △ROQ

⇒  ∠SPO=∠QRO                [ Alternate angles between parallel lines are equal ]

⇒  ∠PSO=∠RQO               [ Alternate angles between parallel lines are equal ]

⇒  ∠POS=∠ROQ          [ Vertically opposite angles ]

∴  △POS≅△ROQ         [ By AAA congruence theorem ]

⇒  segPO≅segRO           [ By CPCT ]

⇒  segSO≅segQO          [ By CPCT ]