Theorems · Theorem · geometry

EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq

∀ {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}, dist p₁ p₂ = dist p₁ p₃ → |(EuclideanGeometry.oangle p₂ p₃ p₁).toReal| < Real.pi / 2

A base angle of an isosceles triangle is acute, oriented angle-at-point form.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

1 results in Mathlib

Foundations

Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented