Either make these constructions with Sketchpad and print them our or construct them with straightedge and compass.
(a) Print a DWEG parallelogram with its diagonal D-segments. Mark the equal angles. Either make the appropriate segments in Sketchpad and print them as thick lines or else color them with a pen on the paper, so the reader can tell what you did.
(b) Print a figure with the D-circles with D-center A through D-points B and C.
(c) Draw the point O and random D-points A and B. Construct an equilateral D-triangle ABC and also a D-square ABDE (on the opposite side of the D-segment AB).
(d) Construct a D-line AB with at least 6 or 7 points on the line equally spaced (in DWEG).
(a) Draw the point O and random D-points A and B. Then construct the D-perpendicular bisector m of the D-segment AB. Hint: m is the D-line which D-reflects A to B. List the details of your construction and explain why it works.
(b) Explain clearly why the D-circles that have D-center A are a family of Apollonian circles (defined by what two points?). Tell a construction for these circles that will construct the D-circle through B with center A as a script using only O, A and B as givens.
(c) If c is an E-circle not through O, is c a D-circle. Explain. If so, what is the center? Also, is any E-line m not through O a D-circle. Explain. If so, what is the center?
(a) Draw two concentric circles (in standard Euclidean geometry) and a third circle between them (just between, not tangent). Then construct at least 4 circles tangent to all 3 of these circles. Sketch how you can construct 8 circles.(b) Explain how (a) can be used to solve the problem of Apollonius.