You forgot to mention what you need to cut and why?

You could cut triangle in many ways. One way is to use knife tool with axis constraint (K, C). Here are some others:

From top row, left to right:

- Loop cutting a triangle is possible by cheating and turning it to a quad momentarily: In the screenshot I’ve selected the top vertex, Ctrl+shift+B to make a vertex bevel and I gave it a little bit of bevel by holding shift while moving mouse. It’s then possible to loop cut and when done, select all and W -> remove doubles. F6 after that if you need to increase the merge distance.
- If you need straight cuts, could select edges from opposite sides and W -> subdivide
- To make it of even smaller triangles, could select the whole triangle and press alt+P to make it a triangle fan