Quiz 2

 

NAME __________________________________________________

 

Question 1: Compositions of Isometries (short answer)

 

Answer with one ore more names indicating all the possible kinds of isometry that are possible consistent with the given information.

 

a)     If S is a glide reflection and T is a line reflection, then ST can be a

 

b)    If U is a translation and V is a glide reflection, then VU can be a

 

c)     Suppose point A is on line m.  Then if M is line reflection in line m and N is point reflection in point A, MN can be a

 

d)    If E is a translation and F is a point reflection, EF can be a

 

Question 2: State a theorem.

 

Write down clearly and correctly the statement of one of the 3 fundamental theorems of isometries (hint: the number 3 figures prominently in two of the theorems).

 

 

Question 3: Answer in complete sentences.

 

a)     What is the definition of an isometry of the plane?

 

 

 

 

 

 

 

b)    If T is an isometry of the plane and ABC is a triangle, why is the image of ABC by T a triangle congruent to ABC?

 

 

 

 

 

 

 

 

 

 

 

c)     If F is a figure in the plane, what is the definition of a symmetry of F?

 

 

 

 

 

 

 

 

 

d)    If A and B are two symmetries of F, why is AB also a symmetry of F (if it must be)?

 

 

 

 

 

 

 

Question 4: (Short answer)

 

In the figure below, all the chords have equal length.  Recall that the notation for rotation with center Z by angle a is Za.

Answer each of these questions.  You do not have to give reasons for your answers.

 

a)     How many rotational symmetries does this figure have (including the identity)?

 

b)    How many line reflection symmetries does this figure have? ______________

 

c)     What is the measure of angle Q9OP1? ___________________________

 

d)    If L1 is line reflection in line OP1 and M9 is line reflection in line OQ9, tell precisely what isometry is the product M9L1. (State defining data or use clear notation.)

 

 

e)     Continuing with L1 and M9 and with L5 = line reflection in OP5, tell precisely what isometry is the product L1L5M9. (State defining data or use clear notation.)

 

 

f)     Tell as precisely as possible:  What isometry is O72M9?

 

Question 5: Construction

Let the rotation S = A240 and let T = B180.  If U = ST, tell what kind of isometry is U and construct its geometric defining data.