How do I make my entire image transparent?

In the picture I had to make a black triangle and then I made the white triangle. I know how to make the text transparent, but I can't do anything with the white triangle. For example if I put the text and the triangle on a white background it looks just like I want it to, but if I put it on any other colored background or a picture I get what you see in the picture I included. I want the white triangle to be transparent, and for it NOT to show the black triangle behind it, but to show the background or really the background of the picture I want to place the logo on top of. 

I think the real solution would be for me to be able to actually just draw the two sides of the black triangle without the entire triangle or all three corners. I just don't know how to do it. 

Please help me figure out what I am doing here. I am sorry for being such a newbie! Any help will be greatly appreciated.