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I have a slanted object with verts aligned along the slanted edge, however I wish to have the verts aligned horizontally (in Global orientation) while still maintaining their alignment with the edge they are placed on.

enter image description here

If I S, Z, 0, this gets them all perfectly in line, but then it changes the shape of object as it pulls all the verts in a bit. If I set the edge as the transform orientation, and use snapping to align the verts, then it aligns them as they are currently are in the screenshot.

In essence, I need to mix the 2 methods to align in Global orientation while maintaining the edge alignment.

Any help would be appreciated.

Thanks

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The best option here IMO is to use a knife tool. Press K and place the knife icon on the vertex to snap to it. Then press C to make a straight cut. Then select the angled edge and press X-->Dissolve Edges.
enter image description here

To align other edge loops to the newly created horizontal one add an edge loop with Ctrl+R, press E and then F.
enter image description here

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