Ozone resonance question?

Why is it that Ozone has to have one single bond and one double? I got a different structure in which the three atoms are arranged in a triangular shape with one bond connecting each to the other. This satisfies their valencies and removes the charge that would arise in case of resonance. Unless it's necessary that one sigma and one pi-bond have to present or sumthin? idk...this has bn buggin me since my school days n i never quite figured it out