G.27 triangle with equal base angles is isosceles — Code

I.6

If two angles of a triangle are equal, the sides subtending the equal angles are also equal.

"""Programmatic construction for Book I, Proposition 6 (I.6).

        If in a triangle two angles be equal to one another, the sides which subtend
        the equal angles will also be equal to one another.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book I, Proposition 6 using geometor.model."""
            model = Model("I.6")

            # 1. Let ABC be a triangle having the angle ABC equal to the angle ACB.
            A = model.set_point(58, -24, classes=["given"], ID="A")
            B = model.set_point(14, -117, classes=["given"], ID="B")
            C = model.set_point(98, -117, classes=["given"], ID="C")

            model.set_segment(A, B)
            model.set_segment(A, C)
            model.set_segment(B, C)
            model.set_polygon([A, B, C])

            # 2. From AB the greater let DB be cut off equal to AC the less; let DC be joined.
            D = model.set_point(46, -50, ID="D")
            model.set_section([A, D, B])
            model.set_segment(A, D)
            model.set_segment(D, B)
            model.set_segment(D, C)

            # 3. Triangle DBC compared with triangle ACB
            model.set_polygon([D, B, C])

            return model


        if __name__ == "__main__":
            construct_g1()