Edit: You can also rather easily see that the original vertex where the smaller triangles meet is inside the second shape and not on its border. This only works if like here you have access to the grid.

Yeah that's what I noticed after staring at it for awhile that putting the smaller triangle inside the larger one and using the grid you can see they aren't similar.

It reminds me of the common failure of many trisection angle constructions where you can't prove that three intersecting arcs/lines cross at the same point and consequently the proof fails.

Playing around with "equivalent" angles and tangents got me the same ##\frac{2}{5} \neq \frac{3}{8}##

If you take a belt and suspenders approach with proofs -- i.e. have a proof two independent ways of proving / verifying something-- then picture proofs frequently make a nice set of suspenders.

I recently saw similar "paradox" regarding an infinite chocolate bar... I'm not good with math proof but I could tell the bar was shorter after you remove a piece.

As a former fence and deck builder, this was apparent by eyeballing down the long sides of each "triangle", where A appears concaved and B appears convexed.

Edit: You don't need the grid for this inspection.