Words that have identical vowel-based rhyme sounds in the tonic syllable. Moreover, that tonic syllable must start with a different consonantal sound.
There are no pure rhymes for "nacho cheese".
Words that have a pure rhyme on their last syllable only.
Apache's
    Apaches
      prodigies
        prodigy's
          strategies
            strategy's

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              Words that "almost" rhyme on the vowel-based rhyme sound of the stressed syllable like: be/eat or maybe/shapely.
              prodigies
                prodigy's
                  anthologies
                    apologies
                      biology's
                        chronologies
                          doxologies
                            pathologies
                              technologies
                                technology's
                                  etiologies
                                    ideologies
                                      methodologies
                                        biotechnologies
                                          biotechnology's
                                            electrobiology's
                                              colonies
                                                colony's

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                                                  Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."