G.216 triangles angle equal — Code¶
If two triangles have one angle equal to one angle, the sides about other angles proportional, and the remaining angles either both less or both not less than a right angle, the triangles is equiangular and will have those angles equal, the sides about which are proportional.
g1.py
"""Programmatic construction for Book VI, Proposition 7 (VI.7 - g1).
Case 1 of Proposition 7: two triangles with one angle equal, sides about other angles proportional, and remaining angles both less than a right angle.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for 0212.g1 (VI.7) using geometor.model."""
model = Model("VI.7.g1")
# 1. Points
A = model.set_point(62, -29, classes=["given"], ID="A")
B = model.set_point(28, -156, classes=["given"], ID="B")
C = model.set_point(147, -174, classes=["given"], ID="C")
G = model.set_point(137.65, -158.05, ID="G")
D = model.set_point(194, -26, classes=["given"], ID="D")
E = model.set_point(177, -94, classes=["given"], ID="E")
F = model.set_point(240, -105, classes=["given"], ID="F")
# 3. Segments
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(A, G)
model.set_segment(G, C)
model.set_segment(A, C)
model.set_segment(B, G)
model.set_segment(D, E)
model.set_segment(E, F)
model.set_segment(F, D)
# 4. Collinear Sections
model.set_section([A, G, C])
# 5. Polygons (Triangles)
model.set_polygon([A, B, C])
model.set_polygon([A, B, G])
model.set_polygon([B, G, C])
model.set_polygon([D, E, F])
# 6. Angles (Wedges)
model.set_wedge(A, B, B, C)
model.set_wedge(B, A, A, C)
model.set_wedge(B, A, A, G)
model.set_wedge(C, A, A, B)
model.set_wedge(G, A, A, B)
model.set_wedge(G, B, B, C)
model.set_wedge(D, E, E, F)
model.set_wedge(E, D, D, F)
model.set_wedge(F, D, D, E)
return model
if __name__ == "__main__":
construct_g1()
g2.py
"""Programmatic construction for Book VI, Proposition 7, Case 2 (VI.7 - g2).
If two triangles have one angle equal to one angle, the sides about other
angles proportional, and the remaining angles both not less than a right angle,
the triangles will be equiangular.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g2() -> Model:
"""Construct the figure for 0213.g1 (VI.7 Case 2) using geometor.model."""
model = Model("VI.7.g2")
# 1. Points
A = model.set_point(83.0, -29.0, classes=["given"], ID="A")
B = model.set_point(23.0, -160.0, classes=["given"], ID="B")
C = model.set_point(108.0, -142.0, classes=["given"], ID="C")
G = model.set_point(104.5, -126.18, ID="G")
D = model.set_point(188.0, -56.0, classes=["given"], ID="D")
E = model.set_point(155.0, -130.0, classes=["given"], ID="E")
F = model.set_point(201.0, -121.0, classes=["given"], ID="F")
# 2. Segments
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(A, C)
model.set_segment(A, G)
model.set_segment(G, C)
model.set_segment(B, G)
model.set_segment(D, E)
model.set_segment(E, F)
model.set_segment(D, F)
# 3. Collinear Sections
model.set_section([A, G, C])
# 4. Polygons
model.set_polygon([A, B, C])
model.set_polygon([A, B, G])
model.set_polygon([B, G, C])
model.set_polygon([D, E, F])
# 5. Angles / Wedges
model.set_wedge(A, B, B, C)
model.set_wedge(B, A, A, C)
model.set_wedge(B, A, A, G)
model.set_wedge(C, B, B, A)
model.set_wedge(G, B, B, A)
model.set_wedge(G, B, B, C)
model.set_wedge(D, E, E, F)
model.set_wedge(E, D, D, F)
model.set_wedge(F, E, E, D)
return model
if __name__ == "__main__":
construct_g2()