Just for the record there are other languages written in a Cyrillic alphabet: Ukrainian, Bulgarian, and some of the languages from the former Yugoslavia. There are some minor differences.
In each case the first couple of words of each line is the name. If you go to the Wikipedia article on Russian alphabet, you can find the common transliteration of the letters. From that the names should become something recognizable. Some of the letters have more than one transliteration, but the name should be recognizable. Google translation will sometimes translate, or try to translate the name, if the name is a common word, so you could get some funny names.
Some other relevant points, much of Poland was under Russian control for a long time, so many Polish records are in Russian.
All that aside, Russian is by far the largest of these countries, so Russian would be the first choice for your matches shown in the query.