Folded left onto right and then top onto bottom, a square sheet gets one straight cut along the dashed red line, from the top folded edge to the right edge. Into how many pieces does the sheet fall when opened?

Opening the folds mirrors the cut in both creases. The cut and its mirror in the horizontal crease make a V that cuts a triangle off the right edge; the vertical crease copies that V onto the left edge. So 2 triangles fall off and the main sheet is left: $2+1=3$.