Definition isosceles A B C :=
 Cong A B B C.

(* Specifications: *)
Lemma isosceles_sym : isosceles A B C -> isosceles C B A.
Lemma isosceles_conga : A<>C -> A<>B -> isosceles A B C -> CongA C A B A C B.
Lemma conga_isosceles : ~ Col A B C -> CongA C A B A C B -> isosceles A B C.
Lemma isosceles_foot__midpoint_conga : forall H, isosceles A B C -> Col H A C -> Perp H B A C -> ~ Col A B C /\ A<>H /\ C<>H /\ Midpoint H A C /\ CongA H B A H B C.