G.236 parallelogram parallelograms diameter — Code

VI.24

In any parallelogram the parallelograms about the diameter are similar both to the whole and to one another.
A E B G F H D K C 
"""Programmatic construction for Book VI, Proposition 24 (VI.24).

        In any parallelogram the parallelograms about the diameter are similar both to
        the whole and to one another.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for 0257.g1 (VI.24) using geometor.model."""
            model = Model("VI.24")

            # 1. Points of parallelogram ABCD, diameter AC, and parallels EK, GH through F
            A = model.set_point(27.0, -29.0, classes=["given"], ID="A")
            E = model.set_point(73.0, -29.0, ID="E")
            B = model.set_point(179.0, -29.0, classes=["given"], ID="B")

            G = model.set_point(30.0, -60.0, ID="G")
            F = model.set_point(76.0, -60.0, ID="F")
            H = model.set_point(182.0, -60.0, ID="H")

            D = model.set_point(35.0, -128.0, classes=["given"], ID="D")
            K = model.set_point(81.0, -128.0, ID="K")
            C = model.set_point(187.0, -128.0, classes=["given"], ID="C")

            # 2. Construction lines
            model.construct_line(A, C)
            model.construct_line(G, H)
            model.construct_line(E, K)

            # 3. Segments and sub-segments
            model.set_segment(A, B)
            model.set_segment(A, E)
            model.set_segment(E, B)

            model.set_segment(G, H)
            model.set_segment(G, F)
            model.set_segment(F, H)

            model.set_segment(D, C)
            model.set_segment(D, K)
            model.set_segment(K, C)

            model.set_segment(A, D)
            model.set_segment(A, G)
            model.set_segment(G, D)

            model.set_segment(E, K)
            model.set_segment(E, F)
            model.set_segment(F, K)

            model.set_segment(B, C)
            model.set_segment(B, H)
            model.set_segment(H, C)

            model.set_segment(A, C)
            model.set_segment(A, F)
            model.set_segment(F, C)

            # 4. Collinear sections
            model.set_section([A, E, B])
            model.set_section([G, F, H])
            model.set_section([D, K, C])
            model.set_section([A, G, D])
            model.set_section([E, F, K])
            model.set_section([B, H, C])
            model.set_section([A, F, C])

            # 5. Parallelograms and Triangles
            model.set_polygon([A, B, C, D])
            model.set_polygon([A, E, F, G])
            model.set_polygon([F, H, C, K])
            model.set_polygon([E, B, H, F])
            model.set_polygon([G, F, K, D])

            model.set_polygon([A, B, C])
            model.set_polygon([A, C, D])
            model.set_polygon([A, F, E])
            model.set_polygon([A, G, F])

            # 6. Angles
            model.set_wedge(A, B, B, D)  # < B A D )
            model.set_wedge(F, A, A, G)  # < A F G )
            model.set_wedge(C, D, D, A)  # < D C A )
            model.set_wedge(A, D, D, C)  # < D A C )

            return model


        if __name__ == "__main__":
            construct_g1()