Theorems · Theorem · geometry

EuclideanGeometry.angle_right_midpoint_eq_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] {p₁ p₂ p₃ : P},
  dist p₃ p₁ = dist p₃ p₂ → EuclideanGeometry.angle p₃ (midpoint ℝ p₁ p₂) p₂ = Real.pi / 2

If M is the midpoint of the segment AB and C is the same distance from A as it is from B then ∠CMB = π / 2.

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine

Cited by

0 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor