Question

Diagonals of a parallelogram bisect each other.
Given : $\square PQRS$ is a parallelogram. Diagonals $PR$ and $QS$ intersect in point $O$.
TO prove : $\text{seg}PO\cong \text{seg}RO,$
$\text{seg}SO\cong \text{seg}QO$

Answer 1

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

In $△POS$ and $△ROQ$

$\Rightarrow$ $\angle SPO=\angle QRO$ [ Alternate angles between parallel lines are equal ]

$\Rightarrow$ $\angle PSO=\angle RQO$ [ Alternate angles between parallel lines are equal ]

$\Rightarrow$ $\angle POS=\angle ROQ$ [ Vertically opposite angles ]

$\therefore$ $△POS\cong △ROQ$ [ By $AAA$ congruence theorem ]

$\Rightarrow$ $segPO\cong segRO$ [ By CPCT ]

$\Rightarrow$ $segSO\cong segQO$ [ By CPCT ]