I see that on Wikipedia the result about altitude in the right triangle saying h^2=pq is called right triangle altitude theorem or geometric mean theorem. WP: Geometric mean theorem
We have also expressions for legs: a^2=pc, b^2=qc.
In some languages they are called Euclid's theorems. Slovak: Euklidova veta German: Satzgruppe des Pythagoras - Kathetensatz des Euklid and Höhensatz des Euklid.
@MartinSleziak I don't recall, and in my opinion it's too trivial to deserve a name haha.. There's a generalization that does have a name: Stewart's theorem.
Well, I never taught high school geometry - but I suppose that when somebody is teaching students about right triangles, it might be useful to have some name. (So that it is clear which result is used.)
It is taught under this name in Slovakia. (And from the German Wikipedia I suppose that the name is common in some other countries too.)
Since I was taught this result under this name, I was curious what name is used in English speaking countries. But from your response I gather that it does not have a name.
@MartinSleziak For all I know, some high-schools might use the name you've been taught. However, Euclid has so many theorems to his name that it's kind of silly to 'use it up' for this theorem. =)
I learnt Stewart's theorem as part of olympiad training; it's not taught in high-school either.
@MartinSleziak: It's of note that this theorem is the simplest way to show that constructible complex numbers are closed under square-roots, since we can construct sqrt(|z|) and angle-bisectors.
