Congruence of Triangles

If $AB=A'B'$, $AC=A'C'$ and $\widehat{A}=\widehat{A'}$, the triangles $\triangle ABC$ and $\triangle A'B'C'$ are congruent.

• Congruence: $\triangle ABC \equiv \triangle A'B'C$, iff $\triangle ABC$ may be transferred onto $\triangle A'B'C'$ by a Rigid Transformation
• Similiance: $\triangle ABC \sim \triangle A'B'C$, iff all (measures of) angles are equal.
• Consequences, Theorems:
  • Correspondent Angles
  • Alternate-Internal Angles
  • Uniqueness of Perpendicular through Point not on the Line
  • Existence of Parallel through Point not on the Line ($P_2$)