G.59 exterior angle and angle sum of a triangle — Code

I.32

In any triangle, an exterior angle equals the sum of the two opposite interior angles, and the three interior angles sum to two right angles.
Euclid's Elements, Book I, Proposition 32 Triangle ABC with side BC produced to D and line CE drawn parallel to AB. A B C D E 
"""GEOMETOR construction for Book I, Proposition 32 (Folio 0331, Graphic 1).

        In any triangle ABC, if one of the sides BC be produced to D, the exterior angle ACD is equal
        to the two interior and opposite angles CAB, ABC, and the three interior angles ABC, BCA, CAB
        are equal to two right angles.
        """

        from geometor.model import Model


        def build_0331_g1() -> Model:
            model = Model("I.32")

            B = model.set_point(-1, 0, classes=["given"], ID="B")
            C = model.set_point(0, 0, classes=["given"], ID="C")
            D = model.set_point(0.9, 0, classes=["given"], ID="D")
            A = model.set_point(-0.4, 1.0, classes=["given"], ID="A")
            E = model.set_point(0.6, 1.0, classes=["given"], ID="E")

            model.construct_line(B, D)
            model.construct_line(A, B)
            model.construct_line(A, C)
            model.construct_line(C, E)

            model.set_segment(A, B)
            model.set_segment(B, C)
            model.set_segment(C, D)
            model.set_segment(B, D)
            model.set_segment(A, C)
            model.set_segment(C, E)

            model.set_polygon([A, B, C])
            model.set_section([B, C, D])

            model.set_wedge(C, A, A, D)
            model.set_wedge(A, C, C, B)
            model.set_wedge(B, A, A, C)
            model.set_wedge(C, B, B, A)
            model.set_wedge(C, A, A, E)
            model.set_wedge(C, E, E, D)

            return model


        if __name__ == "__main__":
            m = build_0331_g1()
            print(f"Constructed {m.name} with {len(m)} elements.")