Theorems · Theorem · geometry

EuclideanGeometry.angle_midpoint_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 : P), p₁ ≠ p₂ → EuclideanGeometry.angle p₁ (midpoint ℝ p₁ p₂) p₂ = Real.pi

If M is the midpoint of the segment AB, then ∠AMB = π.

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine

Cited by

1 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor