Grade 10 · Math · Geometry

10th grade Symmetry of polygons: lines of symmetry and rotations that map a shape onto itself worksheet

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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 rhombus that is not a square
- A parallelogram with no right angles or equal sides
- A rectangle 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 parallelogram with no right angles
- A square
- A rhombus that is not 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?
- An isosceles trapezoid
- A parallelogram with no right angles and unequal sides
- A rhombus that is not a square
- A rectangle that is not a square
5.
Kira turns a regular hexagon ABCDEF, labeled counterclockwise, 120° counterclockwise about its center. It lands on itself. Where does corner A go?
- D
- B
- E
- C
6.
Luz turns a regular octagon ABCDEFGH, labeled counterclockwise, 135° counterclockwise about its center. It lands on itself. Where does corner B go?
- F
- G
- C
- 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
- C
- D
- A
Pia's regular polygon fits onto itself after a smallest turn of 36°. How many of its lines of symmetry go through two opposite corners?
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?
Tala's regular polygon fits onto itself after a smallest turn of 45°. How many of its lines of symmetry go through two opposite corners?

10th grade Symmetry of polygons: lines of symmetry and rotations that map a shape onto itself worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Symmetry of polygons. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can list every rotation and reflection that carries a figure onto itself, with each mirror line and each center and angle, and decide the list from coordinates.
I can say what two reflections make and where the center is, and use a symmetry as the reason in a short proof.
I can find a counterexample to a claim about symmetry.

Standard: G-CO.A.3

Words to know

line of symmetry (mirror line): A fold line where the two halves match exactly.

rotational symmetry: A turn of less than 360° about the center maps the shape onto itself.

smallest turn (angle of rotation): The least turn that does it; for a regular n-gon, 360° ÷ n.

point symmetry: A half turn, 180°, about the center maps the shape onto itself.

regular polygon: All sides equal and all angles equal.

center: The point the shape turns about; for a parallelogram, where the diagonals cross.

Common mistakes

Your child gave the symmetries of a square for a rectangle or rhombus. A square has 4 lines and a quarter turn; the others have 2 lines and a half turn.

Your child mixed up the lines of a rectangle (through side midpoints) with those of a rhombus (along the diagonals).

Your child expected a slanted parallelogram to have a line of symmetry. Cut one out and try folding it.

Questions parents ask

What is the most common mistake with symmetry of polygons: lines of symmetry and rotations that map a shape onto itself?

Your child gave the symmetries of a square for a rectangle or rhombus. A square has 4 lines and a quarter turn; the others have 2 lines and a half turn.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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