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If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

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Let the angle at which the transversal intersects the lines be `theta`
So, `/_BAD=theta`, `/_EBA=180−theta`
`OB` bisects the `/_EBA` and `OA` bisects the `/_BAD`.
Consider `/_\AOB`, `/_BAO=theta/2`
`/_OBA=1/2(180−theta)=90−theta/2`
`/_BAO+/_OBA+/_BOA=180°`
`=>90−theta/2+theta/2`
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