Escaping the Guillotine and Transitioning to Triangle from Half Guard has never been easier. Here the process is explained, by staying on your side instead of on your back. This way you can still move to a half guard position and begin the transition to Triangle.
Once you are up next to your opponent you can throw one leg up on their back. Once in that position, you can get the other leg up around the head. Move the leg around the waist up to the head to join the other and you have a complete Triangle. Here you can see the move done slowly and with explanations so you can master the move as well.