Symmetry & Tessellation questions for Primary 5 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 rhombus that is not a square have?

   Answer: 2

   The two diagonals of a rhombus are its lines of symmetry: 2 in all.

2. How many lines of symmetry does a parallelogram that is not a rectangle or rhombus have?

   Answer: 0

   A slanted parallelogram has rotational symmetry but no line of symmetry: 0.

3. How many lines of symmetry does an isosceles triangle have?

   Answer: 1

   One line runs from the apex down to the middle of the base: 1 line of symmetry.

4. Which capital letter has exactly two lines of symmetry?

   Answer: X

   A capital X folds onto itself both vertically and horizontally: 2 lines.

5. Which of these regular shapes will NOT tessellate on its own?

   Answer: Regular pentagon

   Each angle of a regular pentagon is 108°, and no whole number of them adds to 360°, so gaps are left.

6. How many lines of symmetry does a regular octagon have?

   Answer: 8

   A regular polygon has as many lines of symmetry as it has sides: 8.

7. Which shape has exactly 4 lines of symmetry?

   Answer: Square

   A square has 4: two through opposite sides and two along its diagonals.

8. A figure is symmetric about a vertical line. A dot sits 3 squares to the left of that line. Where is its matching dot?

   Answer: 3 squares to the right

   A mirror image sits the same distance on the opposite side: 3 squares to the right.

9. How many equilateral triangles meet at a point in a tessellation?

   Answer: 6

   Each angle is 60°, and 360 ÷ 60 = 6 triangles meet at each point.

10. Which of these has no line of symmetry?

    Answer: Scalene triangle

    A scalene triangle has three different sides, so it cannot be folded onto itself.