1. The problem is to understand and apply the triangle postulates to determine if two triangles are congruent. 2. The main triangle 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. - AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent. - HL (Hypotenuse-Leg for right triangles): If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent. 3. To apply these postulates, identify the given parts of the triangles and check if they satisfy any of the above conditions. 4. For example, if you know three sides of two triangles are equal, use SSS to conclude the triangles are congruent. 5. This helps in proving properties about triangles and solving geometric problems involving triangle congruence. Final answer: Use the appropriate triangle postulate (SSS, SAS, ASA, AAS, or HL) based on the given information to determine triangle congruence.