Intercept BE=AB on BD and connect EM. Certificate △ ABM △ EBM (SAS), so ∠A=∠BEM. Because AB//CD, ∠ A+∠ C = 180. Because ∠ BEM+∠ MED = 180, ∠C=∠MED. Certificate △ med △ MCD (AAS), so CD=ED. So BD=BE+ED=AB+CD.