Homer's Theorem: Is It True?

This assessment is based on one of the episodes on The Simpsons, one in which Homer Simpson finds a pair of glasses that apparently makes him super smart the moment he puts them on – or does it? Homer states that “the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side”, which sounds very similar to the Pythagorean theorem. In this assessment, students explore whether Homer’s statement could be true for isosceles or non-isosceles triangles. As they work through the mathematics, they not only become familiar with the triangle inequality, they also learn about and briefly explore degenerate triangles (at achievement level 7-8).