G.244 right angled triangles — Code

VI.31

In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle.

"""Programmatic construction for Book VI, Proposition 31 (VI.31).

        In right-angled triangles the figure on the side subtending the right angle is equal
        to the similar and similarly described figures on the sides containing the right angle.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for 0275.g1 (VI.31) using geometor.model."""
            model = Model("VI.31")

            # 1. Vertices of right-angled triangle ABC and altitude foot D
            A = model.set_point(85.0, -65.0, classes=["given"], ID="A")
            B = model.set_point(46.0, -139.0, classes=["given"], ID="B")
            C = model.set_point(221.0, -139.0, classes=["given"], ID="C")
            D = model.set_point(85.0, -139.0, ID="D")

            # Outer vertices of the three similar rectangles on BC, BA, AC
            B1 = model.set_point(46.0, -202.0, ID="B1")
            C1 = model.set_point(221.0, -202.0, ID="C1")
            B2 = model.set_point(17.0, -124.0, ID="B2")
            A2 = model.set_point(56.0, -50.0, ID="A2")
            A3 = model.set_point(111.0, -16.0, ID="A3")
            C3 = model.set_point(246.0, -90.0, ID="C3")

            # 2. Construction Lines
            model.construct_line(B, C)
            model.construct_line(A, D)

            # 3. Segments of triangle ABC and altitude AD
            model.set_segment(A, B)
            model.set_segment(A, C)
            model.set_segment(B, C)
            model.set_segment(B, D)
            model.set_segment(D, C)
            model.set_segment(A, D)

            # Segments of similar figures on BC, BA, AC
            model.set_segment(B, B1)
            model.set_segment(B1, C1)
            model.set_segment(C1, C)

            model.set_segment(B, B2)
            model.set_segment(B2, A2)
            model.set_segment(A2, A)

            model.set_segment(A, A3)
            model.set_segment(A3, C3)
            model.set_segment(C3, C)

            # 4. Collinear Section along hypotenuse BC
            model.set_section([B, D, C])

            # 5. Polygons (Triangles and similar figures on the three sides)
            model.set_polygon([A, B, C])
            model.set_polygon([A, B, D])
            model.set_polygon([A, D, C])
            model.set_polygon([B, C, C1, B1])
            model.set_polygon([B, A, A2, B2])
            model.set_polygon([A, C, C3, A3])

            # 6. Angles (Wedges)
            model.set_wedge(A, C, C, B)  # Right angle BAC

            return model


        if __name__ == "__main__":
            construct_g1()