Theorems · Theorem · geometry

EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left

∀ {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 p₁ p₃ = 0

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

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor