Symmetry & Tessellation questions for Primary 6 Maths

Every answer with the reasoning behind it. Worth reading after you have tried the set — or on its own, if you are a parent marking it.

1. How many lines of symmetry does a regular pentagon have?

   Answer: 5

   A regular polygon has as many lines of symmetry as it has sides: 5.

2. What is the order of rotational symmetry of a regular hexagon?

   Answer: 6

   A regular hexagon looks the same 6 times in a full turn, so its order is 6.

3. Which capital letter has no line of symmetry?

   Answer: N

   A capital N has rotational symmetry but no line of symmetry.

4. How many squares meet at a point in a tessellation of squares?

   Answer: 4

   Each angle is 90°, and 360 ÷ 90 = 4 squares meet at each point.

5. How many lines of symmetry does a rectangle that is not a square have?

   Answer: 2

   A non-square rectangle folds in half along its length and along its width: 2 lines.

6. What is the order of rotational symmetry of an equilateral triangle?

   Answer: 3

   An equilateral triangle looks the same 3 times in a full turn, so its order is 3.

7. Which of these regular shapes tessellates on its own?

   Answer: Regular hexagon

   Each angle of a regular hexagon is 120°, and 3 × 120° = 360°, so they tessellate.

8. A figure is symmetric about a horizontal line. A mark sits 5 squares above that line. Where is its matching mark?

   Answer: 5 squares below

   A mirror image sits the same distance on the opposite side: 5 squares below.

9. Which shape has infinitely many lines of symmetry?

   Answer: Circle

   Any diameter of a circle is a line of symmetry, and there are infinitely many of them.

10. A shape looks the same after a turn of 90°, 180° and 270°. What is its order of rotational symmetry?

    Answer: 4

    360 ÷ 90 = 4, so the order is 4 — the same as a square.