G.213 equiangular triangles sides — Code¶
In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which subtend the equal angles.
"""Programmatic construction for Book VI, Proposition 4 (VI.4).
In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which subtend the equal angles.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for 0207.g1 (VI.4) using geometor.model."""
model = Model("VI.4")
# 1. Points
A = model.set_point(147, -74, classes=["given"], ID="A")
B = model.set_point(19, -171, classes=["given"], ID="B")
C = model.set_point(168, -171, classes=["given"], ID="C")
D = model.set_point(235.87, -119.57, classes=["given"], ID="D")
E = model.set_point(247, -171, classes=["given"], ID="E")
F = model.set_point(214.87, -22.57, ID="F")
# 2. Construction Lines
model.construct_line(B, E)
model.construct_line(B, F)
model.construct_line(E, F)
# 3. Segments
model.set_segment(B, A)
model.set_segment(A, F)
model.set_segment(B, F)
model.set_segment(B, C)
model.set_segment(C, E)
model.set_segment(B, E)
model.set_segment(F, D)
model.set_segment(D, E)
model.set_segment(F, E)
model.set_segment(A, C)
model.set_segment(C, D)
# 4. Collinear Sections
model.set_section([B, A, F])
model.set_section([B, C, E])
model.set_section([F, D, E])
# 5. Polygons (Triangles and Parallelogram)
model.set_polygon([A, B, C])
model.set_polygon([D, C, E])
model.set_polygon([F, B, E])
model.set_polygon([F, A, C, D])
# 6. Angles (Wedges)
model.set_wedge(B, A, A, C)
model.set_wedge(A, B, B, C)
model.set_wedge(C, A, A, B)
model.set_wedge(C, D, D, E)
model.set_wedge(D, C, C, E)
model.set_wedge(E, C, C, D)
return model
if __name__ == "__main__":
construct_g1()