angle_eq_of_congruent — Mathlib

English

If two polygons are congruent, corresponding angles are equal.

Русский

Если два многоугольника конгруэнтны, соответствующие углы равны.

LaTeX

$$$\text{If } v_1 \cong v_2 \text{ then } \angle(vi) = \angle(v'i)$ for corresponding vertices.$$

Lean4

/-- Corresponding angles are equal for congruent triangles. -/
theorem angle_eq_of_congruent (h : v₁ ≅ v₂) (i j k : ι) : ∠ (v₁ i) (v₁ j) (v₁ k) = ∠ (v₂ i) (v₂ j) (v₂ k) :=
  by
  unfold EuclideanGeometry.angle
  unfold InnerProductGeometry.angle
  simp_rw [real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, vsub_sub_vsub_cancel_right, ←
    dist_eq_norm_vsub, h.dist_eq]

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