Theorems · Theorem · geometry

Wbtw.oangle_sign_eq_of_ne_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] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
  {p₁ p₂ p₃ : P} (p₄ : P),
  Wbtw ℝ p₁ p₂ p₃ → p₁ ≠ p₂ → (EuclideanGeometry.oangle p₁ p₄ p₂).sign = (EuclideanGeometry.oangle p₁ p₄ p₃).sign

Given three points in weak order on the same line, with the first not equal to the second, and a fourth point, the angles at the fourth point between the first and second or first and third points have the same sign.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

2 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented