High definition MKV files

ok , here is my question. I have been downloading some bluray,720,1080,hi def ect in the form of MKV. They play just fine on my computer. Now, what would I need to play these files to view on my high def TV? And what media can I burn these files on and what software will do the trick? Some of the files that I’m downloading are more than 8 Gig. That won’t fit on a reg dvd and i don’t want to compremise the quality. So , If someone can acurately steer me in the rigtht direction , that would be appreaciated.

Build an HTPC for cheap and use it to play any number of file types on your HDTV.

… or try something like this or this.