Theorems · Theorem · geometry

EuclideanGeometry.dist_eq_of_angle_eq_angle_of_angle_ne_pi

∀ {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 = EuclideanGeometry.angle p₁ p₃ p₂ →
    EuclideanGeometry.angle p₂ p₁ p₃ ≠ Real.pi → dist p₁ p₂ = dist p₁ p₃

Converse of pons asinorum, angle-at-point form.

Defined in

Mathlib.Geometry.Euclidean.Triangle

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor