Section TriangleMidpointsTheorems.
Context `{TE:Tarski_euclidean}.

Lemma triangle_mid_par_flat_cong : forall A B C P Q R,
B <> A ->
C <> A ->
C <> B ->
Col A B C ->
Midpoint P B C ->
Midpoint Q A C ->
Midpoint R A B ->
Par A B Q P /\ Par A C P R /\ Par B C Q R /\
Cong A R P Q /\ Cong B R P Q /\ Cong A Q P R /\ Cong C Q P R /\ Cong B P Q R /\ Cong C P Q R.