Congruence in Triangles

May 20, 2024

Congruence in Triangles

Breaking Up Triangles

  • Rather than stacking triangles, it's recommended to break them up.
  • Redrawing triangles helps to visualize congruent angles and sides.

Congruence Notation

  • Angles can be labeled in multiple ways:
    • Direct angle notation (e.g., ∠J ≅ ∠H)
    • Using three-point notation (e.g., ∠JKG ≅ ∠HKG)
    • Prime notation (e.g., ∠G' ≅ ∠K')
  • Side lengths should also be labeled and compared to determine congruence.

Example Breakdown

  • Angle Congruence:
    • ∠J ≅ ∠H (both have 90 degrees)
    • ∠K ≅ ∠G
    • Use prime and three-point notation to avoid confusion with angle names.
  • Side Length Congruence:
    • Side lengths are compared after breaking up the triangles:
      • JJG ≅ HK
      • GK ≅ KG
      • JK ≅ HG

Congruence Statements

  • Triangles are congruent if all corresponding angles and sides are congruent.
  • Example given:
    • ΔGJK ≅ ΔKHG

Common Mistakes

  • Be cautious when labeling triangles and angles.
  • Ensure corresponding angles and sides are correctly identified to avoid errors. For instance, ΔGJK is not congruent to ΔGHK unless corresponding angles and sides match correctly.