Play the MKV files by connecting a USB flash drive directly to your television set. Certain models of HDTV -- like those from Samsung and Panasonic -- support playing many types of audio and video files, including MKV files, directly off of a flash drive or external hard drive. Check your manual to see if your TV supports this. If it does, copy the MKV file to a flash drive and plug your flash drive into the TV.
Stream the MKV files to your TV via a device like an Xbox 360 or PlayStation 3. Install a program like VLC Media Player or PS3 Media Server on your computer. Add the MKV files you want to play to the media server and stream them directly to the console. The program on your computer converts the file into a format that the console can read.
Use your computer as an external monitor for your TV. Use a blue VGA cable, a white DVI cable or an HDMI cable to connect your television set directly to the back of your computer. This allows you to use your TV the same way you would use a computer monitor. Open the MKV file on your computer using a compatible program like VLC or Windows Media Player. The video will play on your TV screen in 720p high definition.