1. Drag the point, X, along the arc shown to illustrate two ways of placing the four triangles on the square mat. In each case, what is the area of the mat not covered by the triangles?[br]2. You can also drag bottom left-hand vertex of the red triangle …[br]3. Write out a proof of Pythagoras’ Theorem arising from your exploration.[br]4. In the applet, the red triangle is fixed while the others move. Describe the motion of the blue triangle, then the green one and finally the yellow one.[br]5. Find the locus of the vertices of these three triangles in turn.