How do I check for triangle triangle intersection?

You could use the built in function called:

OnCollisionEnter(), OnCollisionExit(), or OnCollisionStay().

Each does something different but the names should be straight forward. These require you to have a collider attached to both objects. Here is some Example code of how you could use this:

 //JavaScript - Collider
 OnCollisionEnter(other : Collision)
 {
   if(other.tag == "Player")//if there person hit is tagged player show this message in the log.
    {
      Debug.Log("Player Hit!");
    }
 }
 
 //C# - Collider
 OnCollisionEnter(Collision other)
 {
   if(other.tag == "Player")//if there person hit is tagged player show this message in the log.
    {
      Debug.Log("Player Hit!");
    }
 }

You could also use:

OnTriggerEnter(), OnTriggerExit(), OnTriggerStay().

This just checks if your object is inside a specifc area. This also requires a collider component attached to only 1 of the objects. It also needs to have the "isTrigger" tick box checked. Here is an example of how you could use this:

 //Javascript - Trigger
 OnTriggerEnter(other : Collider)
 {
   if(other.gameObject.tag == "Player")//checks if there person entering is tagged "player"
    {
      Debug.Log("Player Entered!");
    }
 }
 
 //C# - Trigger
 OnTriggerEnter(Collider other)
 {
   if(other.gameObject.tag == "Player")//checks if there person entering is tagged "player"
    {
      Debug.Log("Player Entered!");
    }
 }