Require Export GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec.
Ltac assert_all := treat_equalities; assert_cols_perm; assert_diffs; assert_congs_perm.
Section TriangleMidpointsTheorems.
Context `{TE:Tarski_euclidean}.

Lemma triangle_mid_par_strict_cong_aux : forall A B C P Q R,
~Col A B C ->
Midpoint P B C ->
Midpoint Q A C ->
Midpoint R A B ->
Par_strict A B Q P  /\ Cong A R P Q /\ Cong B R P Q .