Students will start by learning what cevians are and what Ceva's theorem says. Here's a great video on that. Next, students will see the proof of Ceva's theorem shown here. After that, students will see three proofs using Ceva's theorem. First, here's a proof that the medians of a triangle are concurrent. Second, here's a proof that the angle bisectors of a triangle are concurrent. Third, here's a proof that the altitudes of a triangle are concurrent.