ANotSmartPerson

Thanks bunches!

thanks lol

I've tried 3, 6, 9, and 12 and none of them worked xd 

I gave up on the problem and apparently the answer is 11, thanks anyways Melody and Rom.

Solution:

We can construct segments of length 1,sqrt2 ,sqrt5 ,sqrt10 ,2 ,2sqrt2 ,sqrt13 ,3 ,3sqrt2  (these can be obtained systematically by considering all lengths of segments from the top left dot to other dots). The following results can be obtained either by inspection or analysis of slope.

For each of 1, sqrt5, sqrt13, 3, there are zero isosceles triangles having it as its base length.
For sqrt10, there is one.
For each of 2sqrt2, 3sqrt2, there are two.
For each of 2, sqrt2, there are three.
This gives a total of 1 + 2 + 2 +3 + 3 = 11  non-congruent isosceles triangles.

There are a lot more than that, I have a hint that says it involves square roots but that's honestly all I know, I might just give up if nobody here understands it either lol (Thanks for trying though :3)

Thank you so much!

Thank you!!! :)

oof I guess I've uhh 'doomed' you all whoopsies...

Thanks!

Thank you, I appreciate it.

Whoops I must've done it wrong....Thank you!