EuclideanGeometry.angle_eq_angle_of_angle_eq_pi_of_angle_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 p₃ p₄ p₅ : P},
EuclideanGeometry.angle p₁ p₅ p₃ = Real.pi →
EuclideanGeometry.angle p₂ p₅ p₄ = Real.pi → EuclideanGeometry.angle p₁ p₅ p₂ = EuclideanGeometry.angle p₃ p₅ p₄Vertical Angles Theorem: angles opposite each other, formed by two intersecting straight lines, are equal.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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.pistatement and proof · 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
- EuclideanGeometry.angle_commproof · cited by 36
- EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_piproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cosphericalproof · cited by 0