Prove that $OM$ is dividing $\angle IOR$ into two. The square $ORIT$ is a oblong . it is given that $TR=IM$, prove that $OM$ is dividing $\angle IOR$ into two equal angles. added my try in the pic: ![enter image description here]( Please I'm stuck a few hours need help.

$\triangle OIM$ is isosceles, $\angle IOM = \angle IMO$

Also since $TM \parallel OR$, from opposite interior angles, $\angle ROM = \angle IMO$,

From here you have the result.