Assignment for Monday, 11/19

Read the rest of Chapter 1 of Brown.

BE PREPARED to do any of these constructions.

In a figure with 3 lines a, b, c. We call the line reflections A, B, C.

1. If the lines are parallel, for any point P, be able to construct ABC(P) and CBA(P).  Also, since ABC and CBA are themselves line reflections in a line d.  Be able to construct d.
2. If the lines are concurrent, for any point P, be able to construct ABC(P) and CBA(P).  Also, since ABC and CBA are themselves line reflections in a line d.  Be able to construct d.
3. For a mirror line m and points P and Q on the same side of m, be able to construct the path of a billiard ball or a light ray (same thing) from P to Q that reflects from m.

Write the answers to the following questions.

1. If ABCD is a kite but not a rhombus, list all the symmetries of ABCD.
2. If ABCD is a rhombus, list all the symmetries of ABCD.
3. If ABCD is a rectangle but not a square, list all the symmetries of ABCD.
4. Tell all the kinds of quadrilaterals that have a line symmetry.  Be simple but very convincing that your list is complete.
5. For a regular n-gon, how many line symmetries does the figure have.  What are they?  How is the case of even n different from odd n?  Also, tell what are the other symmetries of a regular n-gon.  What is the total number of symmetries.