Theorems · Theorem · geometry

EuclideanGeometry.dist_eq_add_dist_of_angle_eq_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 = Real.pi → dist p₁ p₃ = dist p₁ p₂ + dist p₃ p₂

If ∠ABC = π, then (dist A C) = (dist A B) + (dist B C).

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine

Cited by

2 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor