Question 1

Consider the following statement: "If three points are collinear, their images after an isometry are also collinear." This statement is:

Accepted Answer

A)  always true. 
B)  sometimes true, depending on the isometry. 
C)  never true. 
A)  always true. 
B)  sometimes true, depending on the isometry. 
C)  never true.

Question 2

For the following Questions , use the table for the Klein 4-group: $\begin{array} { l | c | c | c | c | } 
o & I & F & T & R \
\hline I & I & F & T & R \
\hline F & F & I & R & T \
\hline T & T & R & I & F \
\hline R & R & T & F & I \
\hline
\end{array}$
-What is the inverse of $F \circ T$ ?

Accepted Answer

The answer of For the following Questions , use the...

Question 3

Draw a strip pattern that has only translation and glide reflection symmetries.

Accepted Answer

The answer of Draw a strip pattern that has only...

Question 4

How many elements are in the symmetry group of a rectangle?

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  8 
A)  2 
B)  3 
C)  4 
D)  8

Question 5

Draw a shape that has exactly five lines of reflection symmetry.

Accepted Answer

Answers ma

Question 6

Suppose a sequence begins with 3, 5 and continues by adding the previous two numbers to get the next number in the sequence. What number comes after 34 in this sequence?

Accepted Answer

A)  55 
B)  56 
C)  57 
D)  58 
A)  55 
B)  56 
C)  57 
D)  58

Question 7

Suppose a wallpaper pattern has no rotations and no reflections, but has a glide reflection. Use the flowchart in the textbook to find the standard notation for the pattern.

Accepted Answer

A)  pg 
B)  cm 
C)  pm 
D)  pgg 
A)  pg 
B)  cm 
C)  pm 
D)  pgg

Question 8

What motions preserve the following strip pattern? Assume the pattern continues in both directions. 응 응 응 응 응 응 응 응

Accepted Answer

A)  reflection 
B)  rotation 
C)  translation 
D)  All of the above. 
A)  reflection 
B)  rotation 
C)  translation 
D)  All of the above.

Question 9

For the following Questions use the table below  for the Klein 4-group (see Example 6): 
$\begin{array} { l | l | l | l | l | } 
0 & I & F & T & R \
\hline I & I & F & T & R \
\hline F & F & I & R & T \
\hline T & T & R & I & F \
\hline R & R & T & F & I \
\hline
\end{array}$
-According to the table, what is the inverse of F?

Accepted Answer

A)  I 
B)  F 
C)  T 
D)  R 
A)  I 
B)  F 
C)  T 
D)  R

Question 10

A rectangle has the dimension L $\times$ W . If a square has the same area to the rectangle, what is the side length of the square?

Accepted Answer

A)  arithmetic mean of L and W 
B)  geometric mean of L and W 
C)  sum of L and W 
D)  Product of L and W 
A)  arithmetic mean of L and W 
B)  geometric mean of L and W 
C)  sum of L and W 
D)  Product of L and W

Question 11

The square below is transformed by an isometry. Which of the following statements is NOT necessarily true?

Accepted Answer

A)  The distance between vertex A and vertex B remain the same after transformation. 
B)  Vertices A, B, C, and D still form a square after transformation. 
C)  Vertex A is still above vertex D after transformation. 
D)  Vertex A is still adjacent to vertex D after transformation. 
A)  The distance between vertex A and vertex B remain the same after transformation. 
B)  Vertices A, B, C, and D still form a square after transformation. 
C)  Vertex A is still above vertex D after transformation. 
D)  Vertex A is still adjacent to vertex D after transformation.

Question 12

What is the geometric mean of 9 and 81?

Accepted Answer

A)  27 
B)  36 
C)  45 
D)  another answer 
A)  27 
B)  36 
C)  45 
D)  another answer

Question 13

What motions preserve the following strip pattern? Assume the pattern continues in both directions. 문 곰 문 곰 문 곰 문 곰

Accepted Answer

A)  translation 
B)  glide reflection 
C)  reflection 
D)  both A and B 
A)  translation 
B)  glide reflection 
C)  reflection 
D)  both A and B

Question 14

For the following Questions use the table below  for the Klein 4-group (see Example 6): 
$\begin{array} { l | l | l | l | l | } 
0 & I & F & T & R \
\hline I & I & F & T & R \
\hline F & F & I & R & T \
\hline T & T & R & I & F \
\hline R & R & T & F & I \
\hline
\end{array}$
-According to the table, what is the inverse of I?

Accepted Answer

A)  I 
B)  F 
C)  T 
D)  R 
A)  I 
B)  F 
C)  T 
D)  R

Question 15

How many elements are in the symmetry group of a square?

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  8 
A)  2 
B)  3 
C)  4 
D)  8

Question 16

Why do imperfect patterns sometimes pose a challenge to the classification scheme?

Accepted Answer

It's difficult to de

Question 17

What is the geometric mean of 4 and 16?

Accepted Answer

A)  8 
B)  10 
C)  12 
D)  another answer 
A)  8 
B)  10 
C)  12 
D)  another answer

Question 18

What is the name of the spiral pattern of shoots, leaves, or seeds around the stem of a plant?

Accepted Answer

The answer of What is the name of the spiral...

Question 19

Is it possible for a wallpaper pattern to have translation, rotation, and glide reflection isometries, but no reflection isometry?

Accepted Answer

A) True 
 B)False

Question 20

How many elements are in the symmetry group of a nonrectangle parallelogram?

Accepted Answer

A)  1 
B)  2 
C)  4 
D)  0 
A)  1 
B)  2 
C)  4 
D)  0

Exam 19: Symmetry and Patterns

Consider the following statement: "If three points are collinear, their images after an isometry are also collinear." This statement is:

For the following Questions , use the table for the Klein 4-group: o I F T R I I F T R F F I R T T T R I F R R T F I -What is the inverse of F∘TF \circ TF∘T ?

Draw a strip pattern that has only translation and glide reflection symmetries.

How many elements are in the symmetry group of a rectangle?

Draw a shape that has exactly five lines of reflection symmetry.

Suppose a sequence begins with 3, 5 and continues by adding the previous two numbers to get the next number in the sequence. What number comes after 34 in this sequence?

Suppose a wallpaper pattern has no rotations and no reflections, but has a glide reflection. Use the flowchart in the textbook to find the standard notation for the pattern.

What motions preserve the following strip pattern? Assume the pattern continues in both directions. 응 응 응 응 응 응 응 응

For the following Questions use the table below for the Klein 4-group (see Example 6): 0 I F T R I I F T R F F I R T T T R I F R R T F I -According to the table, what is the inverse of F?

A rectangle has the dimension L ×\times× W . If a square has the same area to the rectangle, what is the side length of the square?

The square below is transformed by an isometry. Which of the following statements is NOT necessarily true?

What is the geometric mean of 9 and 81?

What motions preserve the following strip pattern? Assume the pattern continues in both directions. 문 곰 문 곰 문 곰 문 곰

For the following Questions use the table below for the Klein 4-group (see Example 6): 0 I F T R I I F T R F F I R T T T R I F R R T F I -According to the table, what is the inverse of I?

How many elements are in the symmetry group of a square?

Why do imperfect patterns sometimes pose a challenge to the classification scheme?

What is the geometric mean of 4 and 16?

What is the name of the spiral pattern of shoots, leaves, or seeds around the stem of a plant?

Is it possible for a wallpaper pattern to have translation, rotation, and glide reflection isometries, but no reflection isometry?

How many elements are in the symmetry group of a nonrectangle parallelogram?

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For the following Questions , use the table for the Klein 4-group: o I F T R I I F T R F F I R T T T R I F R R T F I -What is the inverse of $F \circ T$ ?

A rectangle has the dimension L $\times$ W . If a square has the same area to the rectangle, what is the side length of the square?