There are actually several "love triangles" in Pride and Prejudice by Jane Austen, although they do not dominate the plot as many of them are only mentioned second-hand.
In the major romance of the book, that between Elizabeth Bennet and Fitzwilliam Darcy, there is in fact a triangle that affects the plot, and especially the motivations of one of the villains of the book. Lady Catherine intends that Darcy marry Anne de Bourgh, and thus resents Elizabeth.
During the period that Darcy is silently in love with Elizabeth, and Elizabeth intrigued by Darcy but still disdainful of him, the oleaginous clergyman William Collins proposes to Elizabeth. When she refuses, he successfully proposes to her friend Charlotte Lucas.
Mr. Bingley's sister Caroline wishes to marry Mr. Darcy, although he has no actual interest in her. This creates and Elizabeth-Caroline-Darcy triangle. It also motivates Caroline to be unpleasant to the Bennet family.
Both of Mr. Bingley's sisters wish him to marry Georgiana Darcy, although he isn't particularly interested in the scheme. That would create a potential Georgiana-Jane-Bingley triangle.
Wickham has eloped with Georgiana, flirted with Elizabeth, and eventually elopes with and marries Lydia.