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copy sketches with history

Is there a way to copy with history, when copied sketches update when the original is changed? If I mirror a sketch without moving it after it is created it will update with the original, as soon as you move the copied sketch it no longer updates. Copy and pasted sketches do not update. I don't want to make a bunch of variable driven copies. Is this even possible? Thanks.
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While you are within a sketch here are the things that do not copy / paste:
What is your end goal? There are usually much better ways of doing things rather than copying sketches.
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These two parts are identical; I only want to define one and have the other one update when I change the original. This is obviously a 3d model, but I want to do the same with a 2d sketch.
Why do you want to copy/update a sketch and not the part? Can you not just copy/modify the 1st part? or build a 2nd part based on the same sketch?
I'm new to parametric drawing/ modeling and I'm starting with sketches and I don't need the 3d model as I will derive dimensions and printable patterns from the 2d sketches.
Multiple sketches take more trouble to manage than configured parts and with more chance of errors. In your case using the same profiles, the the frame tool can give consistant profiles. It's worth the effort to learn OS as a parametric tool instead of fiddling with sketches. Will also provide a visual check of part fits as you go. Attached is a simple sample to give the idea.
https://cad.onshape.com/documents/e7deb849eaf79cbe21dd8d77/w/d33b9654867f8aafb9a49fde/e/20ca0d02e03dccd9b365d82a
You can do configurations with 2D sketches. no need to futz with copy/paste.
Oh I just reread what you are trying to do… Depending on the context of what you ultimately want to do (big pitcture). your sketch for that example would just contain a construction line at 45° from the corner to use as a symmetry line for the symmetry constraints you'd need. Then everything would update based on the modification of one of the sides of the sketch. You could also do it in 2 sketches if you wanted.