1. The problem is to understand the triangle congruence postulates SSS, SAS, and ASA and see examples for each. 2. Triangle congruence postulates are rules that allow us to determine when two triangles are congruent, meaning they have exactly the same size and shape. 3. The three postulates are: - SSS (Side-Side-Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. - SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. - ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. 4. Examples: **SSS Example:** Triangle ABC with sides $AB=5$, $BC=7$, $CA=6$ and triangle DEF with sides $DE=5$, $EF=7$, $FD=6$ are congruent by SSS. **SAS Example:** Triangle ABC with sides $AB=5$, $AC=6$ and included angle $\angle BAC=60^\circ$ and triangle DEF with sides $DE=5$, $DF=6$ and included angle $\angle EDF=60^\circ$ are congruent by SAS. **ASA Example:** Triangle ABC with angles $\angle BAC=60^\circ$, $\angle ABC=50^\circ$ and side $AB=5$ and triangle DEF with angles $\angle EDF=60^\circ$, $\angle DEF=50^\circ$ and side $DE=5$ are congruent by ASA. These postulates help us prove triangle congruence without needing to know all sides and angles.