---- that was rather silly ---- We can do

six:
start with isosceles ACD cut AC and AD at third length yielding b,d and c,e. Find B by intersecting cd with eD and E by intersecting cd with Cb.

Things we can't do:

Making consecutive red-blue-red (OP colors) triangles equal: For example, X=Adc,Y=AcE,Z=Ecb. Because X and Y have the same height and area their bases must be equal, i.e. dc = cE. Similarly cb = cA. But that means that dA and bE are parallel, contradiction.

This still leaves open the possibility of

seven triangles, though.