The Trio, (Cup, Saucer & Plate)

The idea of a Trio is an English one, the Cup was used for one's Tea, the Saucer was to stop drips and spills, and to act a partial insulation should someone happen to put it down on a polished wood surface.

The Tea [Side] Plate, usually around 7" in diameter was used for the bite-size cucumber sandwiches, biscuit or cake.
The plate also enables one to catch the crumbs when eating without having to juggle a cup of hot tea at the same time or indeed the crumbs ending up in the Tea, which is never very satisfactory, or elegant.

Today, the side plate is most often used to go besides the dinner or luncheon plate for bread & butter, bread roll, side salads & the like.

For some reason the American market was developed without the Side Plate, and indeed most modern sets Worldwide are now sold without a Side Plate, these being seen as an "extra".

NB: Confusingly the term "Trio" is also used to describe a set where there is a Tea Cup, Coffee Cup/Can, and a Saucer, these sets usually date from the 18th and early 19th Century, being essentially two cups & one saucer, once seen, these cannot be mistaken for what has been described above.