Symmetry of polygons: lines of symmetry and rotations that map a shape onto itself

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

1.
Ari sketches a four-sided shape with exactly 2 lines of symmetry and no right angles. Which shape is it?
- A rectangle that is not a square
- A parallelogram with no right angles or equal sides
- A rhombus that is not a square
- A square
2.
Bo draws a four-sided shape with 4 right angles and exactly 2 lines of symmetry. Which shape is it?
- A rectangle that is not a square
- A rhombus that is not a square
- A parallelogram with no right angles
- A square
3.
Esme draws a trapezoid with exactly 1 line of symmetry. What must be true about it?
- Its two parallel sides are equal
- Its two slanted sides are equal
- It has four right angles
- Both pairs of opposite sides are parallel
4.
Jun says a shape maps onto itself by a half turn but has no line of symmetry. Which four-sided shape fits?
- A rhombus that is not a square
- A rectangle that is not a square
- A parallelogram with no right angles and unequal sides
- An isosceles trapezoid
5.
Kira turns a regular hexagon ABCDEF, labeled counterclockwise, 120° counterclockwise about its center. It lands on itself. Where does corner A go?
- C
- E
- D
- B
6.
Luz turns a regular octagon ABCDEFGH, labeled counterclockwise, 135° counterclockwise about its center. It lands on itself. Where does corner B go?
- C
- F
- G
- E
7.
Milo turns a regular pentagon ABCDE, labeled counterclockwise, 216° counterclockwise about its center. It lands on itself. Where does corner B go?
- E
- D
- A
- C
8.
Noah turns a regular nonagon ABCDEFGHI, labeled counterclockwise, 120° counterclockwise about its center. It lands on itself. Where does corner C go?
- G
- I
- F
- D
Ren's regular polygon fits onto itself after a smallest turn of 30°. How many of its lines of symmetry go through two opposite corners?
Zee's regular polygon fits onto itself after a smallest turn of 20°. How many of its lines of symmetry go through two opposite corners?

Symmetry of polygons: lines of symmetry and rotations that map a shape onto itself

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1.
Ari sketches a four-sided shape with exactly 2 lines of symmetry and no right angles. Which shape is it?
- A rectangle that is not a square
- A parallelogram with no right angles or equal sides
- A rhombus that is not a square
- A square
2.
Bo draws a four-sided shape with 4 right angles and exactly 2 lines of symmetry. Which shape is it?
- A rectangle that is not a square
- A rhombus that is not a square
- A parallelogram with no right angles
- A square
3.
Esme draws a trapezoid with exactly 1 line of symmetry. What must be true about it?
- Its two parallel sides are equal
- Its two slanted sides are equal
- It has four right angles
- Both pairs of opposite sides are parallel
4.
Jun says a shape maps onto itself by a half turn but has no line of symmetry. Which four-sided shape fits?
- A rhombus that is not a square
- A rectangle that is not a square
- A parallelogram with no right angles and unequal sides
- An isosceles trapezoid
5.
Kira turns a regular hexagon ABCDEF, labeled counterclockwise, 120° counterclockwise about its center. It lands on itself. Where does corner A go?
- C
- E
- D
- B
6.
Luz turns a regular octagon ABCDEFGH, labeled counterclockwise, 135° counterclockwise about its center. It lands on itself. Where does corner B go?
- C
- F
- G
- E
7.
Milo turns a regular pentagon ABCDE, labeled counterclockwise, 216° counterclockwise about its center. It lands on itself. Where does corner B go?
- E
- D
- A
- C
8.
Noah turns a regular nonagon ABCDEFGHI, labeled counterclockwise, 120° counterclockwise about its center. It lands on itself. Where does corner C go?
- G
- I
- F
- D
Ren's regular polygon fits onto itself after a smallest turn of 30°. How many of its lines of symmetry go through two opposite corners?
6
Zee's regular polygon fits onto itself after a smallest turn of 20°. How many of its lines of symmetry go through two opposite corners?
9