Study Questions for Semi-Quiz B

(from the email list)

I expect that you will have a chance to either state the definition of a concept or one of the theorems in Brown.

Also, you really, really need to know the types of isometries (see Fundamental Theorem 3). There are four major kinds of isometries, with the identity as a fifth special case of either translation or rotation, and also with point reflection (halfturn) as a special case of rotation.

In addition to problem solving, there may be a couple of short-answer questions like these:

Short-Answer Questions 1:

From the list of 6 kinds of isometries:

• -Which kinds of isometries preserve orientation (are all double line reflections)?

• -Which kinds of isometries reverse orientation (these are either single or triple line reflections)?

• -If you compose (take the product of) a glide reflection and a rotation, what kind(s) of isometry can the product be?

• -If you take the product of a glide reflection and a point reflection, what kind(s) of isometry can the product be?

• -If you take the product of a point reflection and a translation, what kind(s) of isometry can the product be?

• -If you take the product of a point reflection and a translation, what kind(s) of isometry can the product be?

• -If you compose two glide reflections, what kind(s) of isometry can the product be?

Short Answer Questions 2:

• If T is an isometry and P is a point, take the sequence of points P, P' =T(P), P'' = T(P'), P''' = T(P'').

• If these four points are distinct and collinear, what kind(s) of isometry can T be?

• If these four points all lie on a circle, what kind(s) of isometry can T be?

• If these four points re not all distinct, what kind(s) of isometry can T be?

Medium Answer Question 3:

• If M is reflection in line m and N is reflection in line m, tell precisely what kind(s) of isometry MN can be and be more specific about centers, argles, distances, directions.

• If an isometry T is the product of two halfturns, what kind of isometry is it? Explain why.

Also, study constructions from labs and class.