You can use 'project geometry' when you have selected a 2D face or plane on which to sketch, this will take care of the lines moving around relative to each other as they are constrained to the line/face picked. The projected geometry will probably be construction lines by default so you will have to change them to non construction lines, then you can extrude them or perform another operation.
Have a look through the tutorials as this will be covered in there.
Hope this helps