For 10 points, name this geometric theorem, named for an ancient Greek mathematician, that compares the sides of a right triangle, often written as a squared plus b squared equals c squared.
The formula for Euclidean distance between two points is derived from this theorem. James Garfield drew a trapezoid to begin his proof of this theorem. Sets of positive integers that satisfy this formula are known as namesake (*) "triples," including 3, 4, and 5. For 10 points, name this geometric theorem, named for an ancient Greek mathematician, that compares the sides of a right triangle, often written as a squared plus b squared equals c squared.
The formula for Euclidean distance between two points is derived from this theorem.
Pythagorean theorem (prompt on "a squared plus b squared equals c squared" before mentioned)