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Identify Reflective Symmetry

In this worksheet, students will identify valid lines of symmetry and define if and where they occur in a range of regular and irregular shapes.

Worksheet Overview

QUESTION 1 of 10

What is reflective symmetry?

 

Reflective symmetry is when a shape or pattern is reflected in a line of symmetry or a mirror line.

The reflected shape will be exactly the same as the original, the same distance from the line of symmetry and the same size.

 

 

What is a line of symmetry?

 

Lines of symmetry are imaginary lines that can be drawn on two-dimensional shape, where the image on either side of the line matches exactly

Where lines of symmetry are drawn on shapes, they are usually represented as a dashed line

 

 

 

e.g. Are these lines of symmetry?

 

Diagram showing two possible examples of shapes with symmetry

 

Imagine that we could fold the square along the dashed line - would both halves of the shape fit perfectly over each other?

 

If so, then we have a line of symmetry.

In the case of the square, they do perfectly match, so the line of symmetry shown here is correct.

 

With the triangle, the shapes on either side of the line are not the same.

Can you see that the triangle on the left of the line is smaller than the one on the right? 

So, the line of symmetry shown on the triangle is not correct.

 

 

 

e.g. How many lines of symmetry does the following shape have?

 

Diamond with a letter A inside

 

This has shape two elements - the outer square and the letter A.

A square has 4 lines of symmetry, whilst the letter A has 1 line of symmetry.

 

When we have two elements present, the lowest number of lines of symmetry is the one we need to use.

 

So in this case, we have one line of symmetry on the combined shape, shown here:

 

Diamond with a letter A inside with a line of symmetry through its centre

 

 

 

e.g. How many lines of symmetry does the following shape have?

 

White hexagon

 

This example is actually easier than the last one.

This is a regular hexagon; remember that 'regular' means all the angles and sides are the same.

 

When we have a regular shape, the number of lines of symmetry is the same as the number of sides present, so this shape has 6 lines of symmetry, shown here:

 

White hexagon with multiple lines of symmetry

 

 

 

In this activity, we will identify valid lines of symmetry and define if and where they occur in a range of regular and irregular shapes. We will also use the logic that the number of lines of symmetry match the number of sides present to solve related problems. 

Read the statement below then type a single word in the space to accurately complete it. 

How many lines of symmetry does a square have?

1

2

3

4

How many lines of symmetry does a rectangle have?

1

2

3

4

Triangles can have differing numbers of lines of symmetry, depending on what type of triangle it is.

 

Read the statements below then type one word in each gap to make each true. 

1

2

3

4

Match each geometric shape on the left with its correct number of lines of symmetry.

Column A

Column B

Rectangle
4 lines of symmetry
Equilateral triangle
2 lines of symmetry
Square
1 line of symmetry
Isosceles trapezium
3 lines of symmetry

Review the shape below:

 

Triangle with a proposed line of symmetry

 

Does the dashed line shown represent a viable line of symmetry? 

Yes

No

Investigate the new shape below:

 

Rectangle with a proposed line of symmetry

 

Does the dashed line shown represent a viable line of symmetry? 

Yes

No

How many lines of symmetry does a regular octagon have?

Explore this shape with two separate elements:

 

Image of a square with a triangle inside

 

How many lines of symmetry does this shape have?

0

1

2

3

4

Finally, investigate this irregular shape with two separate elements to complete:

 

White rectangle with a blue cross inside

 

How many lines of symmetry does this shape have?

  • Question 1

Read the statement below then type a single word in the space to accurately complete it. 

CORRECT ANSWER
EDDIE SAYS
Did you recall this essential definition of a line of symmetry from the Introduction and your previous learning? A line of symmetry has to be in a place on a 2D shape so that if you put a mirror on the line, the representation on both sides would be exactly the same. This is why lines of symmetry are also referred to as 'reflective symmetry'. Let's put this theory into practice now in the rest of this activity...
  • Question 2

How many lines of symmetry does a square have?

CORRECT ANSWER
4
EDDIE SAYS
A square has four right-angled corners and four sides which are all exactly the same. This also means that it is a regular shape. When we are working with a regular shape, we know that the number of lines of symmetry will match the number of sides. So it stands to reason that a square will have four lines of symmetry. Can you draw their location on a mental picture of a square in your mind's eye?
  • Question 3

How many lines of symmetry does a rectangle have?

CORRECT ANSWER
2
EDDIE SAYS
Did this one catch you out? Yes, a rectangle has four sides like a square but it is not regular as all the sides are not the same length. A rectangle has one horizontal line of symmetry through its centre, and one vertical - so two in total. If we fold a rectangle diagonally, can you see that both sides don't match up?
  • Question 4

Triangles can have differing numbers of lines of symmetry, depending on what type of triangle it is.

 

Read the statements below then type one word in each gap to make each true. 

CORRECT ANSWER
EDDIE SAYS
An equilateral triangle is a regular shape as it has three sides of equal length, so it will have three lines of symmetry. An isosceles triangle is irregular as it only has two sides which are the same length. This means that it has only one line of symmetry, which would pass horizontally through its centre. A scalene triangle is also irregular as it has no equal sides. This means that it would not be possible to draw a line of symmetry through this shape which would create a mirror image on both sides. Try to imagine doing this mentally now - can you see how that would be impossible to do?
  • Question 5

Match each geometric shape on the left with its correct number of lines of symmetry.

CORRECT ANSWER

Column A

Column B

Rectangle
2 lines of symmetry
Equilateral triangle
3 lines of symmetry
Square
4 lines of symmetry
Isosceles trapezium
1 line of symmetry
EDDIE SAYS
Which of the four shapes are regular? The square and equilateral triangle are, so their lines of symmetry will match their number of sides. Rectangles are irregular, so have just two lines of symmetry - one horizontally through the centre and one vertically. An isosceles trapezium is one in which the base angles are equal and, therefore, the left and right side lengths are also equal. This shape will have one vertical line of symmetry passing through its centre, like this:
  • Question 6

Review the shape below:

 

Triangle with a proposed line of symmetry

 

Does the dashed line shown represent a viable line of symmetry? 

CORRECT ANSWER
No
EDDIE SAYS
Imagine placing a mirror on the dashed line. Would you see a trapezium shape reflected upwards, or a triangle reflected below? No, because the upper and lower sections of this triangle are fundamentally different. A vertical line of symmetry would work, but this was not offered. Before moving on, try explaining to an imaginary friend why this is not a viable line of symmetry.
  • Question 7

Investigate the new shape below:

 

Rectangle with a proposed line of symmetry

 

Does the dashed line shown represent a viable line of symmetry? 

CORRECT ANSWER
No
EDDIE SAYS
Imagine placing a mirror on the dashed line once more. Would you see a right-angled triangle reflected upwards or below? No, you would not. Before moving on, try explaining to an imaginary friend where viable lines of symmetry could be drawn on this rectangle, instead of this diagonal.
  • Question 8

How many lines of symmetry does a regular octagon have?

CORRECT ANSWER
8
Eight
EDDIE SAYS
There's a couple of hints in this question: Regular - All sides are the same length, so this shape will have the same number of lines of symmetry as it does sides. Octagon - What does the prefix 'oct-' mean? 'Oct-' means eight, so we know that this shape will also have eight lines of symmetry, as it is regular.
  • Question 9

Explore this shape with two separate elements:

 

Image of a square with a triangle inside

 

How many lines of symmetry does this shape have?

CORRECT ANSWER
1
EDDIE SAYS
There are two shapes within this one image: an outer square and an inner triangle. The square has 4 lines of symmetry The triangle (which is an isosceles triangle) has 1. Which of these options will the combined shape have? We need to always choose the lower option for combined shapes, so this image has only one line of symmetry.
  • Question 10

Finally, investigate this irregular shape with two separate elements to complete:

 

White rectangle with a blue cross inside

 

How many lines of symmetry does this shape have?

CORRECT ANSWER
2
Two
EDDIE SAYS
There are two shapes here again within this one image: an outer rectangle and an inner, blue cross. The rectangle has 2 lines of symmetry (vertical and horizontal), as does the cross. This means that the combined shape will have the same number as both shapes on this occasion - two lines of symmetry. Congratulations! You can now identify valid lines of symmetry and define if and where they occur in a range of regular and irregular shapes.
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