End PerpBisect_2.
Hint Resolve perp_bisect_cong_1 perp_bisect_cong_2 : cong.
Section PerpBisect_3.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma perp_bisect_cong2 :
forall P Q A B,
Perp_bisect P Q A B ->
Cong A P B P /\ Cong A Q B Q.