Exam 19: Symmetry and Patterns

Assume the following patterns continue in both directions. Which of these patterns has a reflection isometry?

For the shape below, determine how many lines of symmetry exist.

In the International Crystallographic Union notation, a letter p indicates that a strip pattern:

Draw a strip pattern that has only translation and rotation symmetries.

If a figure has translation symmetry and reflection symmetry across the translation line, it:

Identify the elements of the symmetry group of a nonequilateral isosceles triangle.

Assume the following pattern continues in both directions. What isometries preserve the pattern?

In the International Crystallographic Union notation, a letter m indicates that a strip pattern:

Which of the following rectangles is an approximate golden rectangle?

Consider the following statement: "If four points form the corners of a square, their images after an isometry will also form a square." This statement is:

How many different wallpaper patterns are possible?

Draw a shape that has both reflection symmetry and rotational symmetry.

The numbers 8 and 13 are consecutive Fibonacci numbers. What is the next Fibonacci number in the sequence?

Consider the sequence built by the following rule: $A _ { 1 } = 1 , A _ { 2 } = 0 , A _ { n + 1 } = A _ { n } + \frac { A _ { n - 1 } } { 2 } \text { for } n \geq 2$ What is $A _ { 4 } ?$

Which of the following rectangles is an approximate golden rectangle?