This week, we learn about the Triangle Inequality, one of the simplest geometric inequalities with many consequences.
How would you use Triangle Inequality to solve the following?
Given quadrilateral \(ABCD\), let \(E\) and \(F\) be the midpoints of \(AD\) and \(BC\) respectively. Show that \[ AB+DC \geq 2 EF. \] Can equality hold? If yes, when?