Section Book_1_part_5.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
(** * Proposition 32 In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. *)
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(** * Proposition 33 The straight lines joining at the extremities equal and parallel straight lines which are in the same directions are themselves also equal and parallel. *)
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(** * Proposition 34 In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas. *)
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Lemma prop_34_1 : forall A B D C,
A <> B /\ A <> D /\ B <> D ->
Parallelogram A B D C -> (CongA A B D D C A /\ CongA B D C C A B) /\ (Cong A B D C /\ Cong A C B D).