#4. Given below is a table for a Desargues configuration, consisting of ten points and ten lines. There are three points on each line, and these points are listed for each of the lines 1-10 in the chart below. If six of the points in Desargues's geometry are chosen as the vertices of two triangles, then one of the other four points will be the center of persectivity, also called the pole. The axis of perspectivity, containing the other three points, is called the polar. (a) Which three lines are concurrent at E? Which two triangles have E as the center of perspectivity? (Be sure to list the corresponding vertices in the correct order.) Draw an illustration which verifies line 5 is the axis of perspectivity in this case. (b) Which lines are parallel to line 9? (c) Find two lines which intersect, even though they are both parallel to a third line. Polars 1 2 3 4 5 6 7 8 9 10 Points EDD B A A A B C G on the FFE C C B D EF H Line GHI GH I J | J JI Poles A B C E F G H I J