Continuity plus zero integral around every triangle forces holomorphicity.Suggest a slogan
Let \(D\subseteq\CC\) be an open disc and let \(f\colon D\to\CC\) be continuous. If \(\int_{\bd T} f(z)\dz = 0\) for every closed triangle \(T\subset D\), then \(f\) is holomorphic on \(D\).
State Morera's theorem.