Debashis Roy
fskilnik Bunuel chetan2u Hi could you please explain how are the 2 combinations (4th and 5th from left in the 2nd row of the seven diagrams) equilateral triangles?
Thanks in advance
Hi
Debashis_Roy !
Thank you for your interest in my problem and also in my solution.

In the figure above I present ONE of the diagrams you have asked about (for the other, the reasoning is the same).
Please note that I must explain to you why the purple segments (here unfortunately they appear as light grey) have the same lengths.
Reason: we have three congruent triangles (shown), by the SAS case (same two sides and intermediate angle) and the purple segments are (in all cases) opposite to the 60-degrees angle.
(We know it is a 60-degrees angle because of the one-one-one corresponding triangles... see the FIRST equilateral triangle presented in my previous solution, also the first and the last ones in the last row!)
If something is still unclear, please let me (us) know!
Regards and success in your studies,
Fabio.