You have a bright son - he's right! A "pyramid" is simply a polygon base (any number of sides) with triangular sides meeting at a common point (the "vertex").
Mostly, when we say "pyramid", we mean what are called "regular pyramids". Regular pyramids are ones where the base is a regular polygon (all sides and angles the same) of any number of sides. The simplest regular pyramid then is a 4-sided pyramid (base + 3 sides). Its proper name is a "tetrahedron". The tetrahedron has the extra interesting property of having all four triangular sides congruent.
An Egyptian pyramid has a square base and four triangular sides. Its proper name is a "square pyramid".
Good for you!
Stephen La Rocque.