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      Lesson details

      Learning outcome

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

      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.

      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.

      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.

      Teacher tip

      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.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      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
      Correct answer: 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

      To help you plan your 9 maths lesson on: Similarity in shapes, download all teaching resources for free and adapt to suit your pupils' needs...