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I have some door trims that need replacing and I want to match them with the rest of the house. I tried doing a straight mitre but they don't look as good and because it's an old house the door isn't perfectly square anymore.

With these which I tried to cut unsuccessfully, a bit of movement out of square doesn't matter because the profile fits into it. But as I say, I've not managed to cut them. I'm sure there is an easy technique. How do you do it?

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It's called "coping", and is done with what else but a coping saw. –  Tester101 Jun 21 at 12:24
    
This looks like a really nice coping job. It would be difficult to get the joint that tight without lots of experience. –  Edwin Jun 22 at 2:25

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Testor101 is correct in both points. Coping this joint with the coping saw is the way it was most likely done when it was built. It does allow for a corner to be a bit of out of square, but doing this will be taxing on the blade of a coping saw, it is a lot of wood to cut through. But it can be done with patience. Trying to rush through a cut this size will break blades.

If you have access to a band saw, it would make it much easier to do, but to get it a tight fit would still require some tweaking. Whether you run the stock at a slight angle after the cut is started to give the cut an extra relief in the back, what I have been taught is "back cut", so the face of the cut is absolutely tight but the mating faces are gapped slightly, but that does not matter since it is not visible. You could use a rasp to tune the cut too. This back cut can be done with the coping saw too.

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