Theorems · Theorem · geometry

EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two

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

An oriented angle in a right-angled triangle (even a degenerate one) has absolute value less than π / 2. The right-angled property is expressed using unoriented angles to cover either orientation of right-angled triangles and include degenerate cases.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle

Cited by

2 results in Mathlib

Foundations

Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented