Section DISTINCT_PARALLEL.

Lemma EmbeddedSimilarTriangles : forall A B C : Point, forall n : nat,
Clockwise A B C ->
n > 0 ->
forall D E : Point,
HalfLine A B D ->
HalfLine A C E ->
Distance A D = DistTimesn n A B ->
Distance A E = DistTimesn n A C ->
Angle A B C = Angle A D E /\ Angle A C B = Angle A E D.