New
New
Year 9

Similarity in shapes

I can recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.

New
New
Year 9

Similarity in shapes

I can recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.

Lesson details

Key learning points

  1. Two shapes are not similar if there is a pair of lengths with a different multiplicative relationship.
  2. Similar shapes are not always easy to spot visually.
  3. A ratio table can help you find the scalar and functional multipliers in similar shapes.
  4. The angle sizes do not change.

Common misconception

Pupils may find it difficult to match up corresponding measurements on two congruent shapes when they are in different orientations.

Look lengths which are between any pairs of known angles or look for angles which are between pairs of adjacent known lengths. Also, tracing paper could be used to reflect/rotate/translate one shape onto the other.

Keywords

  • Object - The object is the starting figure before a transformation has been applied.

  • Image - The image is the resulting figure after a transformation has been applied.

  • Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

To demonstrate that angles in a triangle can always be read in the same order (either by going clockwise or anticlockwise around the vertices) ask three pupils to stand in a triangle. Then ask them to try to rearrange their order so that they are not stood next to the same person.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
When an object is enlarged by a scale factor of 2, the object and its image are __________.
alternate
congruent
corresponding
Correct answer: similar
supplementary
Q2.
A triangle is enlarged by a scale factor of 2. Which of the following measurements will remain invariant?
Correct answer: the angles
the length of its base
the length of its height
its perimeter
Q3.
Which angles are always equal when found on figure containing parallel lines and a transversal?
adjacent
Correct answer: alternate
co-interior
Correct answer: corresponding
Q4.
Which angle is corresponding with ∠ECD?
An image in a quiz
∠ACE
∠CEH
∠FEC
Correct answer: ∠GEF
Q5.
Which rectangle is not similar to rectangle R?
An image in a quiz
A
Correct answer: B
C
Q6.
Triangle B is an enlargement of triangle A. What is the scale factor?
An image in a quiz
10
Correct answer: 12
15

6 Questions

Q1.
Which triangle is not similar to the others?
An image in a quiz
A
Correct answer: B
C
D
Q2.
The table shows the base and height of four rectangles. Which rectangle is similar to a rectangle that is 2 cm by 5 cm?
An image in a quiz
A
B
C
Correct answer: D
Q3.
Which shape is similar to shape P?
An image in a quiz
A
B
C
Q4.
The length of EB is cm.
An image in a quiz
Correct Answer: 3, three, 3 cm, 3cm
Q5.
The length of CD is cm.
An image in a quiz
Correct Answer: 8, eight, 8cm, 8 cm
Q6.
∆ABC is similar to ∆ACD. The value of $$x$$ is .
An image in a quiz
Correct Answer: 24, twenty four, 24 cm, 24cm