Similar.angle_eq
∀ {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_4} {P₂ : Type u_5} [inst : NormedAddCommGroup V₁]
[inst_1 : NormedAddCommGroup V₂] [inst_2 : InnerProductSpace ℝ V₁] [inst_3 : InnerProductSpace ℝ V₂]
[inst_4 : MetricSpace P₁] [inst_5 : MetricSpace P₂] [inst_6 : NormedAddTorsor V₁ P₁] [inst_7 : NormedAddTorsor V₂ P₂]
{a b c : P₁} {a' b' c' : P₂},
Similar ![a, b, c] ![a', b', c'] → EuclideanGeometry.angle a b c = EuclideanGeometry.angle a' b' c'For two similar triangles, the corresponding angles are equal.
- Defined in
- Mathlib.Geometry.Euclidean.Similarity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- Nat.cast_zeroproof · cited by 1,870
- Real.piproof · cited by 1,774
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- one_ne_zeroproof · cited by 885
- Matrix.vecConsstatement and proof · cited by 852
Cited by1
Results whose statement or proof uses this declaration.
- Similar.angle_eq_allproof · cited by 0