Final answer:
Prospero's dialogue in Act IV, Scene i, lines 139-142 and Act V, Scene i, lines 33-57 of 'The Tempest' are monologues. Ariel's speech in Act IV, Scene i, lines 171-184 is a soliloquy.
Step-by-step explanation:
When analyzing character dialogue in Shakespeare's plays, distinctions between a soliloquy, an aside, and a monologue are vital. In The Tempest, particularly in Act IV, Scene i, lines 139-142, Prospero's speech is defined as a monologue because he speaks at length to convey his thoughts while other characters are on stage. In contrast, Act IV, Scene i, lines 171-184 showcases Ariel's lines as a soliloquy since it is a speech made when the character is alone on stage. Further into the play, in Act V, Scene i, lines 33-57, Prospero's extended speech is again considered a monologue since it's directed to other characters that are present even if they do not participate in the dialogue.