G.214 triangles sides proportional — Code¶
If two triangles have their sides proportional, the triangles is equiangular and will have those angles equal which the corresponding sides subtend.
g1.py
"""Programmatic construction for Book VI, Proposition 5 (VI.5 - g1).
Given triangle ABC in Proposition 5.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for 0209.g1 (VI.5) using geometor.model."""
model = Model("VI.5.g1")
# 1. Points
A = model.set_point(131, -49, classes=["given"], ID="A")
B = model.set_point(26, -151, classes=["given"], ID="B")
C = model.set_point(103, -136, classes=["given"], ID="C")
# 3. Segments
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(C, A)
# 5. Polygons (Triangle)
model.set_polygon([A, B, C])
# 6. Angles (Wedges)
model.set_wedge(A, B, B, C)
model.set_wedge(B, A, A, C)
model.set_wedge(C, A, A, B)
return model
if __name__ == "__main__":
construct_g1()
g2.py
"""Programmatic construction for Book VI, Proposition 5 (VI.5 - g2).
Triangles DEF and GEF constructed on common side EF in Proposition 5.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g2() -> Model:
"""Construct the figure for 0209.g2 (VI.5) using geometor.model."""
model = Model("VI.5.g2")
# 1. Points
D = model.set_point(84, -29, classes=["given"], ID="D")
E = model.set_point(27, -83, classes=["given"], ID="E")
F = model.set_point(69, -75, classes=["given"], ID="F")
G = model.set_point(105, -106, ID="G")
# 3. Segments
model.set_segment(D, E)
model.set_segment(E, F)
model.set_segment(F, D)
model.set_segment(G, E)
model.set_segment(G, F)
# 5. Polygons (Triangles)
model.set_polygon([D, E, F])
model.set_polygon([G, E, F])
# 6. Angles (Wedges)
model.set_wedge(D, E, E, F)
model.set_wedge(E, D, D, F)
model.set_wedge(F, D, D, E)
model.set_wedge(E, F, F, G)
model.set_wedge(F, E, E, G)
model.set_wedge(G, E, E, F)
return model
if __name__ == "__main__":
construct_g2()