Create a plane that bisects two line segments

I am using SW2014 SP5.

Is there a selection method to create a plane that bisects two line segments at their intersection without creating additional reference sketch entities? The attached picture will clarify:

I want to create the plane shown by just making selections in the "red" sketch - at the intersection, perpendicular to the plane of the sketch, at the angle that bisects the two lines. I had to create the green sketch to make this work.

My reasoning is that I have to create multiple planes like this and I am trying to avoid adding a secondary reference sketch at every intersection. I have attached a simple file for your convenience.

Thanks,

Daen

SolidworksParts And Features