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What is the best way to go about cutting MDF where two pieces of the cab share the same line (such as in Lusid's Plans)? I don't want pieces to be 1/16th off when I go to put it together

I think the reason you aren't getting any replies is that your question is too general. To provide help we need to better understand what tools you have available to you. The "best" way to cut MDf would be with a large CNC machine and a vac table or perhaps a sliding table saw but of course most people don't have easy access to those tools. Likewise, a good quality tracksaw does a very nice job as well even for long pieces. If you can provide some info as to what tools you have for cutting MDF sheets we can provide better guidance. Do you have a tablesaw with a fence? Do you have a circular saw that could be guided with an inexpensive straight edge? Generally those approaches are going to give you a better result than an unguided options like a jigsaw.

You misunderstood the question. It's not about which tool to use, it's about where to cut.
He's got a plan like this:

Now the question is whether the line is part of the board to cut or not. If it's part of the board, you would cut close to the line, leaving it intact. However, if you cut like this, cutting out board A would remove the thickness of your sawblade + the thickness of the line from board B.
So the answer to his question is to cut on the line, thereby removing equal parts from board A and board B.

However, this is probably moot because the OP didn't bother to log in for 6 days.

Add the width of the saw's teeth or blades to your cutting measurements, to allow for "wastage".

Ok. Well figuring out that would simply require looking at the whole plan and doing whatever you chose to do symmetrically. This is wood we are talking about here so the issue of the saw kerf is likely not a big deal provided you do the same thing to each side. Given that many table saw blades are 1/8", and that is the likely largest kerf you are going to be making, you are talking at most about building a box 1/8 inch larger or smaller than the plan defines. If there are critical tolerances in a standup cabinet less than 1/8" I would be surprised. However, that should be pretty evident from the whole plan.


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