Every shape can be cut exactly in half with one straight line

For any bounded planar region with positive area, sliding a line of any fixed orientation yields a continuous area function that attains half the total, guaranteeing an exact bisecting line in that direction. A right-triangle example shows a horizontal line through its centroid splits the area 44.4%/55.6%. Additionally, one straight line can bisect two independent shapes simultaneously, illustrating the two-dimensional Ham Sandwich theorem.