Elementary projective geometry is just the geometry of a line, or straightedge. It was introduced by Pappus around 300 A.D., and is ideally suited for K-6 education. This video introduces some basic notions: the join of two points, and the meet of two lines, and definitions of side, vertex, triangle and trilateral. Then we examine a remarkable correspondence between quadrangles and quadrilaterals. The three diagonal points and diagonal sides feature prominently in this construction.
You will want to follow along with these constructions, on your own piece of paper with a pen or pencil and ruler.