Cross's (Vecten's) theorem
First try and explain why (prove) it is true yourself. But if you get stuck, have a look at the (unedited) proof of one of my Kennesaw graduate students at Gin Chou's proof
Then explore the analogous cases below and also try to explain why (prove) why they are true. (Each one below, except the last, has a link to an article of mine on the topic).