2.2 Symmetry

Worked example 2

Colour the squares to make a symmetrical pattern where the dashed line is a line of symmetry.

line of symmetry symmetrical

Reflect the shaded squares across the mirror line.

Answer: Place a small mirror along the mirror line to see what the complete symmetrical pattern will look like.

Squares that are next to the mirror line are reflected to squares that are next to the mirror line on the other side. Squares that are one square away from the mirror line are reflected to squares that are one square away from the mirror line on the other side.

Exercise 2.2

Focus 1 Spot the difference.

Draw shapes on the right side of the picture to make it a reflection of the picture on the left.

Tip

Place a small mirror on the mirror line. Check that the picture on the right looks the same as the image in the mirror.

mirror line

2 Zara says that she is thinking of a triangle with three lines of symmetry. Draw a ring around the name of the triangle that Zara is thinking of. scalene isosceles equilateral right-angled

3 Shade squares to make a pattern with one line of symmetry. mirror line

4 Predict where the reflection of the triangle will be after it is reflected over each of the mirror lines. Draw your predictions using a ruler.

mirror line

mirror line

mirror line

mirror line

Check your predictions by placing a mirror along each of the mirror lines in turn. Look at how the triangle is reflected. Tick the predicted reflections that are correct. Use a different colour pencil to correct the predictions that are wrong.

Practice 5 Use a ruler to draw all of the lines of symmetry on these triangles.

A B

C D

E

6 Shade 5 squares in each of the empty quadrants to make a pattern with two lines of symmetry. mirror line

mirror line

7 Reflect the square, triangle, rectangle and pentagon over both the horizontal and vertical mirror lines until you make a pattern with reflective symmetry. mirror line

mirror line

Challenge 8 Choose four colours. Use coloured pencils or pens to shade in the squares and half squares marked with a star (*).

Reflect the pattern over the mirror lines and colour all the squares to make a pattern with two lines of symmetry.

mirror line

Tip

You could rotate the pattern so that the mirror lines appear vertical and horizontal.

mirror line

9 Sofia says that a right-angled triangle cannot have a line of symmetry. a Draw a triangle to show that Sofia is wrong.

b Write the name of the triangle you have drawn and draw the line of symmetry onto it.

10 This is a chessboard. a How many lines of symmetry does a chessboard have?

b Where could you place a counter on the chessboard so that the chessboard still has two lines of symmetry? Mark the place with a blue circle. c Where could you place a counter on the chessboard so that the chessboard has no lines of symmetry? Mark the place with a red circle. d Where could you place a counter on the chessboard so that the chessboard has only one line of symmetry?

Mark the place with a green circle.

11 a Colour two more squares so that this pattern has exactly 1 line of symmetry.

b Colour two more squares so that this pattern has exactly 2 lines of symmetry.

c What is the fewest number of squares that have to be shaded to make this pattern have exactly 4 lines of symmetry?

Shade the grid to show your solution.