Practice Maths

Topic Review — Symmetry

Mixed Practice — Lessons 64–65

This review covers Lessons 64–65: Line Symmetry and Rotational Symmetry. Try each question before checking your answers.

Review Questions

  1. Lines of Symmetry Fluency

    State the number of lines of symmetry for each shape or letter.

    (a) Regular octagon
    (b) Kite
    (c) Scalene triangle
    (d) Square
    T
    (e) Letter T
    Z
    (f) Letter Z
    (g) Heptagon (7 sides)
    (h) Rhombus

  2. Rotational Symmetry Fluency

    State the order and minimum angle of rotation for each shape. The red dot marks the centre of rotation. Write “order 1, no rotational symmetry” where appropriate.

    (a) Regular octagon
    (b) Rectangle
    (c) Equilateral triangle
    (d) Rhombus
    (e) Circle
    (f) Scalene triangle

  3. Line vs Rotational Understanding

    For each shape, state the number of lines of symmetry AND the order of rotational symmetry.

    (a) Parallelogram
    (b) Rhombus
    (c) Regular pentagon
    (d) Isosceles triangle
    (e) Square

  4. Mixed Problems Understanding

    1. A shape has exactly 3 lines of symmetry and order 3 rotational symmetry. Name it.
    2. A shape has 2 lines of symmetry and order 2 rotational symmetry but is NOT a square. Name two possibilities.
    3. What is the minimum angle of rotation for a regular 9-gon (nonagon)?
    4. True or False: every shape with line symmetry also has rotational symmetry.

  5. Problem Solving Problem Solving

    1. A logo designer wants a shape with exactly 4 lines of symmetry and order 4 rotational symmetry. Name two suitable shapes.
    2. A spinner has 8 equal sectors. What is the order of rotational symmetry? If you rotate it 45°, does it look the same?
    3. Explain why a parallelogram has rotational symmetry of order 2 but no line symmetry.
    4. A shape is reflected in the y-axis. The original had a vertex at (3, 2). Where is the new vertex?

  6. Alphabet Symmetry Fluency

    For each capital letter, state the number of lines of symmetry:

    H
    (a) Letter H
    A
    (b) Letter A
    S
    (c) Letter S
    O
    (d) Letter O
    1. Which capital letters have rotational symmetry of order 2 but no line symmetry?

  7. Lines of Symmetry in Regular Polygons Fluency

    State the number of lines of symmetry for each polygon, then answer the pattern question.

    (a) Equilateral triangle
    (b) Regular hexagon
    (c) Regular decagon
    1. What pattern do you notice? Write a rule for a regular polygon with n sides.

  8. Rotational Symmetry in Real Life Understanding

    1. A ceiling fan has 4 equally spaced blades. What is the order of rotational symmetry? What is the minimum angle?
    2. A company logo has order 6 rotational symmetry. What angle do you rotate through each time?
    3. Name two objects you use every day that have rotational symmetry. State the order for each.

  9. Create Symmetric Designs Understanding

    1. Describe a design using only squares and triangles that has exactly 2 lines of symmetry and order 2 rotational symmetry.
    2. Can a shape have rotational symmetry without having any lines of symmetry? Give an example.
    3. Can a shape have lines of symmetry without having rotational symmetry (order > 1)? Give an example.

  10. Symmetry in Coordinates Problem Solving

    1. A shape has a line of symmetry along the y-axis. One vertex is at (3, 5). What is the location of the corresponding vertex on the other side?
    2. A shape has a line of symmetry along the x-axis. One vertex is at (−2, 4). What is the location of the mirror vertex?
    3. A triangle has vertices at (2, 0), (6, 0), and (4, 5). Does it have a line of symmetry? If so, describe it.
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