Theorems · Theorem · geometry

EuclideanGeometry.angle_add_angle_eq_of_sbtw

∀ {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] {a c p x : P},
  Sbtw ℝ a x c → EuclideanGeometry.angle a p x + EuclideanGeometry.angle x p c = EuclideanGeometry.angle a p c

If X lies strictly between A and C, then ∠ A P X + ∠ X P C = ∠ A P C, with no nondegeneracy assumption on the point P.

Defined in

Mathlib.Geometry.Euclidean.Triangle

Cited by

1 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor