I'm not sure if 'split path at intersection' is the correct term, but I think it's close enough. I am trying to get the image on the right to be like the image on the left. The crazy part is that I already did the image on the left on accident, but cannot remember how I did it and have now spent half my life trying to duplicate the process. I have the small jagged section overlapping the triangle and need the one on the right to slice where they intersect so it looks like the left. Clear as mud? Thanks...!!! Hopefully the image appears because I've never posted here before.

Hi.
I believe Path->Division is what you´re looking for:


Cheers

In Inkscape, there is often more than one way to do something. If you have a top piece on the right, that's like the top piece on the left, here's how you could use that piece to do this.

Position the top piece on top of the triangle - like it looks like you already have it.

-- duplicate the top piece
-- hold the Shift key and click on the large triangle, so that both are selected
-- Path menu > Difference

The duplicated piece disappears, it's sort of consumed in the process of cutting into the large triangle. So now you have the large triangle, cut like you want, and the original top piece. You can drag them apart now, if you want to.

I'm sure we could come up with even more ways to do this

Thank you both! I got it finally