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.