What dice to use in a game that revolves around triangles?
Doing some research shows you will still 5-9 range but it will be slightly more when you are using d4. Now if that difference causes a problem that would be up to you to decide. One other thing to note is you will no longer be able to roll a 2.

This comes from https://anydice.com/program/51b6



#    |  % for 2d6   |  % for 3d4   |
2    |   2.777778   |     0.0000   |
3    |   5.555556   |     1.5625   |
4    |   8.333333   |     4.6875   |
5    |   11.11111   |     9.3750   |
6    |   13.88889   |     15.625   |
7    |   16.66667   |     18.750   |
8    |   13.88889   |     18.750   |
9    |   11.11111   |     15.625   |
10   |   8.333333   |     9.3750   |
11   |   5.555556   |     4.6875   |
12   |   2.777778   |     1.5625   |