Theorems · Theorem · geometry

EuclideanGeometry.angle_add_of_ne_of_ne

∀ {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] {a b c p : P},
  a ≠ b →
    a ≠ c → Wbtw ℝ b p c → EuclideanGeometry.angle b a p + EuclideanGeometry.angle p a c = EuclideanGeometry.angle b a c

Given a triangle ABC with A ≠ B and A ≠ C and a point P on BC, ∠ B A P + ∠ P A C = ∠ B A C.

Defined in

Mathlib.Geometry.Euclidean.Triangle

Cited by

1 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor