(** Given two angles a and b such that a/2 + b/2 is acute, a/2 + b/2 = (a+b)/2 *)

Lemma suma_preserves_ghalfa : forall A B C D E F X Y Z A' B' C' D' E' F' X' Y' Z',
Acute X Y Z ->
SumA A B C D E F X Y Z -> SumA A' B' C' D' E' F' X' Y' Z' ->
gHalfA A B C A' B' C' -> gHalfA D E F D' E' F' ->
gHalfA X Y Z X' Y' Z'.