Triangles are the hardest for me, especially big ones. Everyone is right about cutting generously - I also put a couple of pins where the seam line will be - not perpendicular to it, as if I'm going to piece, but pins to mimic the stitches I'm about to make, then fold the fabric over and hold it up to the light to make sure it will actually cover what I want it to with an adequate seam allowance as well. If not I reposition and try again or cut a new piece of fabric. This saves a lot of ripped stitches.
The more confident I become of my paper piecing, the less I have to pre-test.