Bisect an object on a flat plane?

I want to bisect an object where the resulting verts all have the same x or y or z value. For example I want all the new verts to have a z value of 15.44. The new verts will have different x and y values.

thanks

Just select your vertices, press Z and 0 [zero] to align them on the z axis. Then move them all along the Z axis to where you want them (G to grab, then Z to constrain to Z axis, look at your numbers in the properties panel to get them to where you want them.)