Uncle Wally welcomes the viewer to Sesame Street. Telly appears to tell Uncle Wally that The Grand High Triangle Lover is coming to Sesame Street today. Telly doesn't know why he is, but just then he appears with his dim-witted assistant Norman. The Grand High Triangle Lover tells Telly that he's thinking that he'd be "The Triangle Lover of the Year." All Telly has to do is show him how much he loves triangles by the time he and Norman get back. They exit, and Telly wonders what to do. He then decides to get his tuba.
Oscar the Grouch witnesses Telly with his pet worm Slimey. Telly explains to Oscar that they're rehearsing a song about how much he loves triangles. Telly plays the tuba and sings while Slimey plays the triangle. They play the song for Oscar, who seems impressed with it. Telly worries that if Oscar likes the song, then everyone else won't. He soon forgets the song idea and decides to approach Savion.
Savion teaches a tap-dancing lesson to some kids. In a panic, Telly asks Savion if he knows any triangle dance. Savion doesn't know any, but he's gotten an idea--for something like a square dance. Pulling out a triangle and giving it to Telly, Savion makes a triangle with his foot as he hits the triangle three times. Then Savion makes the dance more complicated, causing Telly to forget it and move on to something else.
Uncle Wally and Savion observe that Telly is taking a nap on a crate. They're relieved that Telly isn't thinking about triangles, until they hear Telly talk about triangles in his sleep.
Telly is now drawing triangles with different colored crayons in a rush. Savion and Uncle Wally tell Telly that even if he's not "Triangle Lover of the Year", he can still have his love for triangles. Telly realizes that and it makes him feel better...
Telly is still making his acceptance speech while it's getting dark. Uncle Wally comes back to take Telly home, but Telly has to finish. Annoyed with Norman's triangle dinging, The Grand High Triangle Lover chases Norman while Uncle Wally announces the sponsors.