New
New
Year 9

Congruent, similar or neither

I can differentiate between shapes which are congruent or similar or neither.

New
New
Year 9

Congruent, similar or neither

I can differentiate between shapes which are congruent or similar or neither.

Lesson details

Key learning points

  1. If two shapes are congruent, then they are similar.
  2. Congruent shapes have a scalar of one.
  3. A ratio table can be a helpful tool for checking the multipliers.
  4. The multiplicative relationship between the sides of the object is preserved in its image.

Common misconception

Pupils may mix up the meanings of congruence and similarity or struggle with the hierarchy of their nested sets (e.g. thinking that all similar shapes are congruent rather than the other way around).

Frequently refer to a Venn diagram showing the set of congruence shapes inside the set of similar shapes when examining pairs of shapes.

Keywords

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

  • Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

Display an ordered checklist for determining the relationship between two shapes. First check if they have the same angles, then check if the angles are in the same order and then check whether the shapes have the same lengths as each other or lengths that are in the same proportions.
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.
Which triangle is congruent to triangle T?
An image in a quiz
Correct answer: A
B
C
Q2.
Which triangle is similar to triangle T, but not congruent to triangle T?
An image in a quiz
A
B
Correct answer: C
Q3.
Rectangle A has lengths 3 cm by 6 cm. Rectangle B is congruent to rectangle A. One of the lengths of rectangle B is 6 cm, so the other length is cm.
Correct Answer: 3, three, 3 cm, 3cm
Q4.
The image shows two congruent pentagons. What is the value of $$x$$?
An image in a quiz
2.9
Correct answer: 3.2
3.4
4.8
Q5.
The image shows two similar hexagons. The size of the angle $$x°$$ is °.
An image in a quiz
Correct Answer: 153, one hundred and fifty three, 153 degrees, 153 deg, 153°
Q6.
Rectangle A has lengths 3 cm by 6 cm. Rectangle B is similar, but not congruent, to rectangle A. One of the lengths of rectangle B is 6 cm, so the other length is cm.
Correct Answer: 12, twelve

6 Questions

Q1.
The two shapes in the image are __________.
An image in a quiz
congruent
Correct answer: similar
neither congruent similar
Q2.
The two shapes in the image are __________.
An image in a quiz
congruent
similar
Correct answer: neither congruent or similar
Q3.
The two shapes in the image are __________.
An image in a quiz
Correct answer: congruent
similar
neither congruent or similar
Q4.
∆ABG and ∆ADE are __________.
An image in a quiz
congruent
Correct answer: similar
neither congruent or similar
Q5.
∆ADE and ∆ACF are __________.
An image in a quiz
congruent
similar
Correct answer: neither congruent or similar
Q6.
∆ABC and ∆CDE are __________.
An image in a quiz
Correct answer: congruent
similar
neither congruent or similar