How did Pythagoras discover the triangle theorem? - Answers

If by "triangle property" you mean the Pythagorean theorem, then your question is so deep, perhaps even deeper than the question why a2 + b2 = c2. The scientists of human behaviour have not yet found what exactly triggers the mind to form or to express a new idea. Exogenous (meaning from the surrounding environment) as well as endogenous (meaning from inside ourselves) factors combine so at specific moment a brilliant idea is formed in the mind of someone. The society and the education where someone lives is one of the major factors. The quality of the brain that each one has, is another major factor. Coincidence should also be regarded.