When first introducing how the corresponding parts in triangles are congruent, I like to relate this to apartments and houses. Most houses in neighborhoods are 1 of 4 different models for the entire neighborhood; the same goes for apartments–they are all under the same floor plan and lay-out. So that if there’s ever damage or a fire to a portion of the house, they can easily repair the house by applying concepts of congruence of the original model houses.
When constructing identical buildings, the architects and construction workers must ensure that the buldings are the same. One way they can make this process simpler is by applying either SSS SAS AAS ASA or HL rather than worrying about all six parts of the triangle.