This applet shows the construction of Pappus' Theorem. Move the slider to see the construction progress. Step 0 shows two lines. You can move the two lines using the diamond-shaped points. Step 1 shows three points on the two lines, labelled correspondingly. You can move these brown points along the lines - even put them "out of order". Step 2 shows transversals meeting in three specific points. Step 3 shows a line through these three points - Pappus' Theorem says these three points are always collinear.