(a) Prove that you can dissect any triangle into four similar triangles. (That is, all four smaller triangles are similar to each other.)
(b) Prove that you can dissect any triangle into six similar triangles.
Can you find numbers other than four and six that always work?
a) After drawing all 3 of the midpoints into a triangle's 3 sides, connect them, and you should be able to prove that the 4 triangles formed are similar to each other.
b) Sorry, but I do not know the answer to this question, good luck regardless.
According to some online resources, you can divide any triangle into 8 similar triangles.