Section DISTINCT_PARALLEL.

Lemma ThreeEmbeddedTriangles : forall A B C D E F G : Point,
Clockwise A B C ->
HalfLine A B D ->
HalfLine A C E ->
Angle A B C = Angle A D E ->
Angle A C B = Angle A E D ->
Between A D F ->
Between A E G ->
Distance D F = Distance A B ->
Distance E G = Distance A C ->
Angle A B C = Angle A F G /\ Angle A C B = Angle A G F.