EuclideanGeometry.exterior_angle_eq_angle_add_angle
- 1000+ list: Exterior angle theorem
∀ {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} (p : P),
Sbtw ℝ p p₁ p₂ → EuclideanGeometry.angle p₃ p₁ p = EuclideanGeometry.angle p₁ p₃ p₂ + EuclideanGeometry.angle p₃ p₂ p₁The Exterior angle theorem. an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
- Defined in
- Mathlib.Geometry.Euclidean.Triangle
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- Nat.cast_zeroproof · cited by 1,870
- Real.piproof · cited by 1,774
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.anglestatement and proof · cited by 187
- neg_eq_zeroproof · cited by 171
- sub_eq_zero_of_eqproof · cited by 154
- Sbtwstatement and proof · cited by 122
- EuclideanGeometry.angle_commproof · cited by 36
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