Theorems · Theorem · geometry

Orientation.norm_eq_of_two_zsmul_oangle_sub_eq

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) {x y : V},
  2 • o.oangle x (x - y) = 2 • o.oangle (y - x) y → o.oangle x y ≠ 0 → o.oangle x y ≠ ↑Real.pi → ‖x‖ = ‖y‖

Converse of pons asinorum, oriented vector angle form (given equality of angles mod π).

Defined in

Mathlib.Geometry.Euclidean.Triangle

Cited by

1 results in Mathlib

Foundations

Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact