I've got two objects which used to be one that I want to join back together. however, the alignment is now off. I'd like to move and rotate the edited object in whatever way is necessary to get their vertices at the edge to match.
In other words, I have a perfectly identical group of vertices on two different objects. I want to move one object so that it's group of vertices match the other.

I've found several ways to match one point, but because the rotation is wrong, none of the other points are aligned correctly.

In the pictures provided, I've selected the vectors that should be matched.

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  • $\begingroup$ If the rotations were changed in object mode you can copy the rotations from the one object to the other so they are easier to align. $\endgroup$ – Brenticus Jan 3 '18 at 0:37
  • $\begingroup$ Choose 3 points, 2 of which on one edge. match the first using one of your methods already used. Use it as a pivot to match other end of edge. Then rotate around that edge to match third. $\endgroup$ – batFINGER Jan 3 '18 at 7:51

I wasn't able to find a way to perfectly align the peices with a snap of sort like I had hoped. That said, I was able to find a method that allowed me to align them to a degree of precision that makes it so that even the part that should be the furthest away is aligned to match exactly to within a millionth of a unit.

  • Snap one vertex
    • Enter Edit mode on the object to be moved (Select it and press Tab)
    • Select one vertex
    • Move the 3D cursor to that spot (Shift + S, Cursor to Active)
    • Exit Edit mode (Press Tab)
    • Set the origin to that point (Shift + Control + Alt + S, Origin to 3D Cursor)
    • Turn on Snap During Transform (Shift + Tab)
    • Set its Type Of Element To Snap To to Vertex (In the header, next to the magnet icon)
    • Set its Part To Snap Onto (just to the right of the Type Of Element To Snap To) to Active
    • Move it until it snaps (G key to move, move your mouse to the vertex that should align)
    • Rotate it most of the way
      In this case, I knew that it was already knew it was aligned on one axis, so I rotated it along that axis (in this case the Z axis). Because the origin is now at the perfectly aligned vertex, it won't move if you set the Pivot Center to work by its origin (On the header, to the right of the mode option and the display method, set to Active Element)
      I rotated along the Z axis (R to start rotating,Z` to then constrain to the Z axis). I got it decently close.
    • Fine tune
      I then zoomed in as close as I could get to the point that would be the furthest away (opposite side of the circle of vertexes) and started editing the object rotation while in Object mode and wireframe view mode (Z while in Object mode). You can find this in the Object section of the Properties window. I just edited the Z rotation little by little until it matched as closely as I could get. After checking, there is zero difference in the position of the vertexes now.

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