Theorems · Theorem · geometry

EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_right

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {p₁ p₂ p₃ : P},
  EuclideanGeometry.angle p₁ p₂ p₃ = Real.pi → EuclideanGeometry.angle p₂ p₃ p₁ = 0

If the angle ∠ABC at a point is π, the angle ∠BCA is 0.

Defined in: Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine
Cited by: 0 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace MetricSpace NormedAddTorsor

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Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
InnerProductSpacestatement and proof · cited by 3,523
Real.pistatement and proof · cited by 1,774
MetricSpacestatement and proof · cited by 1,684
NormedAddTorsorstatement and proof · cited by 1,325
EuclideanGeometry.anglestatement and proof · cited by 187
EuclideanGeometry.angle_commproof · cited by 36
EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_leftproof · cited by 1

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