Lab Report 9 (Due Wednesday 12/4)

The questions for this report can also be found in the text of Lab 9 (in red) and will be clearer in that context.

Problem 1. Include a printout of problem below, or else do a version by straightedge and compass construction with general circles and point A. Turn in as Problem 1 of Report 9.

1. Solve this problem. Draw a sketch with a point A and two circles c and d. The problem is to find all points P on c and Q on d so that A is the midpoint of PQ. Carry out a solution with Sketchpad, inspired by the previous problem. What are the possible numbers of solutions PQ?

Problem 2. Write a proof that the composition of two half turns is a translation.

Problem 3. Explain why the equation H_D = H_C H_B H_A implies that ABCD is a parallelogram.

Problem 4A Draw a general quadrilateral and use it to tessellate the plane. Either cut out a cardboard shape and trace around it to draw congruent copies, or cut out multiple (congruent) copies of a general quadrilateral and tape them to a piece of paper showing how the quadrilateral tessellates the plane. There are parts 4B and 4C below with addition features to add to this tessellation.

Problem 4B. Draw the midpoint quadrilaterals onto your quadilateral tessellation in Problem 4.

Problem 4C. On your quadrilateral tessellation of Problem 4A, mark the centers of rotation. Are there any line reflections for a general quadrllateral? Mark a fundamental domain for TRANSLATIONS for this tessellation.

Finally, tell what is the name of the wallpaper pattern for this tessellation. (See Farmer.)