Theorems · Theorem · geometry

EuclideanGeometry.oangle_homothety

∀ {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)]
  (p p₁ p₂ p₃ : P) {r : ℝ},
  r ≠ 0 →
    EuclideanGeometry.oangle ((AffineMap.homothety p r) p₁) ((AffineMap.homothety p r) p₂)
        ((AffineMap.homothety p r) p₃) =
      EuclideanGeometry.oangle p₁ p₂ p₃

A homothety with a nonzero scale factor preserves angles.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

0 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented