NAME ___________________________________

Math 444 Semi-Quiz B

Question 1: Fundamental Theorem 3 proves that every isometry of the plane is one of several types of isometry.

List all the names of the types of isometry in this theorem:

If you did not include them in your list, also add Identity and Point Reflection to your list to make a (possibly) longer list.

Question 2: From your longer list from Question 1, write the name of each type of isometry in one of these two columns to indicate whether it is orientation-preserving or orientation reversing.

orientation-preserving

orientation reversing

Question 3: In each case, write the name(s) of all the possible types that the product isometry can be. Suppose that F and G are glide reflections, L and M are line reflections, S and R are rotations.

a) What type of isometry can MR be? __________________________________

b) What type of isometry can FG be? __________________________________

c) What type of isometry can LSM be? __________________________________

d) What type of isometry can LML be? __________________________________

Question 4: Let m, n, p, q be 4 lines; denote the reflections in the line by R_m, R_n, R_p, R_q.

Solve this equation of isometry products to write R_q as a product of the others.

R_m R_q R_n = R_p

Question 5: In the figure, point A is on line m. Construct a line n so that R_mR_n = A₆₀.

(Notation: R_m and R_n are reflections in lines m and n. A₆₀ denotes rotation with center A and angle 60 degrees.)