Euclidean geometry | Theorems about special triangles | Articles containing proofs | Elementary geometry
Pons asinorum
In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (Latin: [ˈpõːs asɪˈnoːrũː], English: /ˈpɒnz ˌæsɪˈnɔːrəm/ PONZ ass-i-NOR-əm), typically translated as "bridge of asses". This statement is Proposition 5 of Book 1 in Euclid's Elements, and is also known as the isosceles triangle theorem. Its converse is also true: if two angles of a triangle are equal, then the sides opposite them are also equal. The term is also applied to the Pythagorean theorem. Pons asinorum is also used metaphorically for a problem or challenge which acts as a test of critical thinking, referring to the "ass' bridge's" ability to separate capable and incapable reasoners. Its first known usage in this context was in 1645. A persistent piece of mathematical folklore claims that an artificial intelligence program discovered an original and more elegant proof of this theorem. In fact, Marvin Minsky recounts that he had rediscovered the (which he was not aware of) by simulating what a mechanical theorem prover might do. (Wikipedia).
