G.39 supplementary adjacent angles form a line — Code¶
If two segments at a point on a line on opposite sides make adjacent angles summing to two right angles, the two segments are collinear.
"""Programmatic construction for Book I, Proposition 14 (I.14)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0290.g1 using geometor.model."""
model = Model("I.14")
# Points
C = model.set_point(5, -79.5, classes=["given"], ID="C")
B = model.set_point(87, -79.5, classes=["given"], ID="B")
D = model.set_point(168, -79.5, classes=["given"], ID="D")
A = model.set_point(58, -22, classes=["given"], ID="A")
E = model.set_point(150, -18, ID="E")
# Construction lines
model.construct_line(C, D)
model.construct_line(A, B)
model.construct_line(B, E)
# Segments
model.set_segment(C, D)
model.set_segment(A, B)
model.set_segment(B, E)
model.set_segment(B, C)
model.set_segment(B, D)
# Collinear / broken sections
model.set_section([C, B, D])
model.set_section([C, B, E])
# Polygons
model.set_polygon([C, B, A])
model.set_polygon([A, B, E])
model.set_polygon([E, B, D])
# Angles (wedges)
model.set_wedge(B, A, A, C)
model.set_wedge(B, A, A, D)
model.set_wedge(B, A, A, E)
model.set_wedge(B, E, E, D)
return model
if __name__ == "__main__":
construct_g1()