Do mitochondria digest fats?

by G.G
(-)

I am a student and I'm currently using the IB biology Oxford textbook. A few weeks ago I had a test on biochemistry. I studied on my textbook and it stated the following: "Mitochondrion: (…) fat is digested here if it is being used as an energy resource in the cell" (page 22) "The energy store from them (Triglycerides) can be released by aerobic cell respiration" (page 78). My teacher told me that I was wrong to write these statements in my test. Is there something wrong? Is the term 'fat' too generic? Do different kinds of fats undergo either aerobic or anaerobic respiration? I am currently confused as I do not know who is right and who is wrong… Can someone answer my questions?

Thank you