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Can I copy one sketch to another plane which is not parallel to the sketch plane?
Yes you can. Choose the sketch to copy > Edit from top of screen, select Copy, select new plane, > Edit and paste to the new plane.
tutorial - how to copy sketch to another plane
Step 1
Exit from sketch and choose sketch from feature tree. then go to Edit>>copy. Be sure that sketch must be closed and selected. if you don't, copy button will be inactive.
Step 2
Open sketch on o plane and Edit>>paste
Step 3
Now you can position. You need to drag and drop holding the lines because if you drag the point, only that point will move.