gen-briefly-explain-congruence-criteria-and-one-common-misconcep-75de

Briefly explain congruence criteria and one common misconception about it.

# Congruence Criteria **Congruence criteria** are conditions that guarantee two triangles are congruent (identical in shape and size). The main criteria are: - **SSS** (Side-Side-Side): All three pairs of corresponding sides are equal - **SAS** (Side-Angle-Side): Two pairs of sides and the included angle are equal - **ASA** (Angle-Side-Angle): Two pairs of angles and the included side are equal - **AAS** (Angle-Angle-Side): Two pairs of angles and a non-included side are equal - **RHS/HL** (Right angle-Hypotenuse-Side): For right triangles only ## Common Misconception **AAA is NOT a congruence criterion.** Many students mistakenly believe that if three angles are equal, the triangles must be congruent. However, **AAA only proves similarity**, not congruence. Triangles with the same angles can be different sizes (like a small and large equilateral triangle—both have 60° angles but aren't congruent). Similarly, **SSA (Side-Side-Angle) is not reliable** for general triangles, as it can produce two different triangles (the ambiguous case).