Question

Two line segments PR and QS bisect each other. Prove that PQRS is a parallelogram. ​

Answer 1

Step-by-step explanation:

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 ]