Isosceles trapezoids, norms and inner products

Generalizing a property of isosceles trapezoids in the real plane, we obtai n a characterization of inner product spaces (i.p.s.). The same property al lows us to give a definition of a new orthogonality relation, which is stud ied in detail and generalizes many of the well-known orthogonalities, e.g. Pythagoras, Birkhoff and James. This orthogonality has the property of bein g empty for 2 dimensional spaces, but we give some examples of 3 dimensiona l spaces, not i.p.s., that admit couples of vectors relationed by our ortho gonality.