I am reading about contact geometry and I have a question: Why do we only consider contact structure of an odd-dimension manifold? and the same question for definition of symplectic geometry?

I think for the contact geometry case, a reason is that we want $\alpha \wedge (d\alpha)^n$ to be a volume form. Am I right? I am not sure about that.

Thank you so much for your help.

P.S there is no tag for Contact-geometry.