Symmetry in Polygons

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Show your work for each problem.

1.
Which shape has exactly $2$ lines of symmetry and rotational symmetry of order $2$ ?
1. a)Kite
2. b)Regular hexagon
3. c)Rectangle
4. d)Square
2.
Which shape has point symmetry?
1. a)Equilateral triangle
2. b)Isosceles trapezoid
3. c)Kite
4. d)Parallelogram
3.
Where do the lines of symmetry of a regular pentagon go?
1. a)A regular pentagon has no lines of symmetry
2. b)Each through the midpoints of two opposite sides
3. c)Each through two opposite vertices
4. d)Each through a vertex and the midpoint of the opposite side
4.
Which shape has rotational symmetry but no line of symmetry?
1. a)Kite
2. b)Rectangle
3. c)Parallelogram (not a rectangle or rhombus)
4. d)Isosceles triangle
5.
Which statement is always true?
1. a)Every polygon with point symmetry has at least one line of symmetry
2. b)A shape with rotational symmetry of order $3$ has point symmetry
3. c)A regular polygon with $n$ sides has rotational symmetry of order $n$
4. d)A kite has rotational symmetry of order $2$
6.
How many lines of symmetry does a regular hexagon have?
7.
What is the smallest angle of rotation of an equilateral triangle, in degrees?
8.
What is the order of rotational symmetry of a rhombus that is not a square?
9.
A regular polygon fits onto itself after a turn of $30°$ , and no smaller turn works. How many lines of symmetry does it have?
10.
A regular decagon has $10$ lines of symmetry. How many of them pass through two opposite vertices?
11.
Describe the symmetry of an isosceles triangle that is not equilateral.
12.
Find the symmetry of a regular pentagon.
13.
A rectangle measures $8$ cm by $5$ cm. Find its symmetry.
14.
Describe the lines of symmetry and the rotational symmetry of a regular dodecagon ( $12$ sides).
15.
Check the symmetry of a kite (that is not a rhombus).
16.
A regular hexagon is turned by $240°$ about its center. How many of its smallest rotation steps is that?
17.
Each interior angle of a regular polygon measures $140°$ . Find its number of lines of symmetry and its smallest angle of rotation.
18.
All lines of symmetry of a regular pentagon pass through its center. What is the angle between two neighboring lines?