Given any five points on a flat surface that are in general position (i.e. no two of them coinciding and no three of them on a straight line), prove that four of these points will always form a convex quadrilateral.
For any five points in general position there exist three points A, B and C such that the lines l1 (between A and B) and l2 (between A and C) divide the plane into four parts, one of which contains all five points. Assume without loss of generality that point A serves as origin of the coordinate plane (which is not necessarily Cartesian plane), l1 represents the y-axis and l2 represents the x-axis, which means all points are in the first quadrant. There are only 2 cases to consider:
Case 1. If one of the other two points is outside the triangle ABC, then you can join it with the BC edge of ABC and a convex quadrilateral is formed.