G.53 equal alternate interior angles imply parallel lines — Code

I.27

If a transversal cutting two lines makes the alternate interior angles equal, the lines are parallel.
Euclid's Elements, Book I, Proposition 27 Straight line EF falling on straight lines AB and CD making alternate angles AEF and EFD equal, with hypothetical meeting at G. A B C D E F G 
"""Programmatic construction for Book I, Proposition 27 (I.27).

        If a straight line falling on two straight lines make the alternate angles equal
        to one another, the straight lines will be parallel to one another.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book I, Proposition 27 (I.27) using geometor.model."""
            model = Model("I.27")

            A = model.set_point(20, -29, classes=["given"], ID="A")
            B = model.set_point(150, -29, classes=["given"], ID="B")
            C = model.set_point(20, -77, classes=["given"], ID="C")
            D = model.set_point(150, -77, classes=["given"], ID="D")
            E = model.set_point(95, -29, classes=["given"], ID="E")
            F = model.set_point(70, -77, classes=["given"], ID="F")
            G = model.set_point(207, -51, ID="G")

            # Lines and transversal
            model.construct_line(A, B)
            model.construct_line(C, D)
            model.construct_line(E, F)

            # Segments and collinear sub-segments
            model.set_segment(A, B)
            model.set_segment(A, E)
            model.set_segment(E, B)
            model.set_section([A, E, B])

            model.set_segment(C, D)
            model.set_segment(C, F)
            model.set_segment(F, D)
            model.set_section([C, F, D])

            model.set_segment(E, F)
            model.set_segment(B, G)
            model.set_segment(D, G)
            model.set_segment(E, G)
            model.set_segment(F, G)

            # Hypothetical triangle GEF in reductio proof
            model.set_polygon([G, E, F])

            # Alternate and exterior/interior angles: < A E F ), < E F D ), < E F G )
            model.set_wedge(E, A, A, F)
            model.set_wedge(F, E, E, D)
            model.set_wedge(F, E, E, G)

            return model


        if __name__ == "__main__":
            construct_g1()