By knowing the three side lengths of the triangle and its image, you can prove congruence.
If congruent, the same multiplicative relationship will exist for each pair of side lengths.
The angle pairs will be the same.

Common misconception

Pupils may believe that knowing the three angles is sufficient to prove two triangles are congruent.

Use an equilateral triangle to show that, although two equilateral triangles have the same angles, they are not guaranteed to be congruent. In fact they are similar.

Keywords

Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

If your pupils need further support or practice, the unit Geometrical properties: similarity and Pythagoras' theorem could be useful. Pupils working on the higher tier may want to concentrate their time on the second learning cycle.

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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Starter quiz

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6 Questions

Q1.

__________ is the multiplier between similar shapes that describes how large one shape is compared to the other.

An enlargement factor

A ratio

Correct answer: A scale factor

A vector

Q2.

This sector is enlarged by scale factor $$\frac{1}{3}$$. The angle in the image is °.

Correct Answer: 60

Q3.

Each square on this coordinate grid is 1 unit long. This object is enlarged by a scale factor of 3 to make its image. The perimeter of the image is cm.

Correct Answer: 11, eleven

Q4.

A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 5. The perimeter of the image is cm.

Correct Answer: 300, 300 cm

Q5.

The object is enlarged by a scale factor of $$\frac{1}{4}$$ to make the image. What is the perimeter of the image?

8.25 cm

11 cm

12.5 cm

Correct answer: 16.5 cm

Q6.

A shape is enlarged by a scale factor of $$\frac{2}{5}$$ to make its image. The perimeter of the image is 28 cm. The perimeter of the object is cm.

Correct Answer: 70, 70 cm

Exit quiz

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6 Questions

Q1.

Alex says, "If one shape can fit exactly on top of another using __________, __________ or translation, then the shapes are congruent." Select the words that correctly complete Alex's statement.

enlargement

Correct answer: reflection

Correct answer: rotation

similarity

transformation

Q2.

Which of these pairs of shapes look like they are congruent to each other?

Correct Answer: An image in a quiz

Q3.

Some Oak pupils are discussing congruence. Which pupils are correct?

Aisha: "All rectangles are similar to each other."

Correct answer: Andeep: "All squares are similar to each other."

Correct answer: Jun: "All equilateral triangles are similar to each other."

Laura: "All pentagons are similar to each other."

Correct answer: Sofia: "All circles are similar to each other."

Q4.

The diagram shows a pair of congruent triangles. The length of the side marked $$x$$ is m.

Correct Answer: 7, seven

Q5.

The diagram shows a pair of congruent triangles. Which of these Oak pupils are making a correct statement?

Correct answer: Alex: "The side marked $$x$$ is 108 mm."

Aisha: "The angle marked $$w$$ is 53°."

Lucas: "The side marked $$y$$ is 85 mm."

Correct answer: Sofia: "The side marked $$z$$ is 85 mm."

Sam: "There is not enough information to find the angle $$w$$°."

Q6.

Select the statements needed to prove the following: "The diagonal of a rhombus bisects the shape into two congruent triangles."

Correct answer: AC = BC = CD = DA as they are edges of a rhombus.

AC = BD as the shape is a rhombus.

AC is a shared edge.

Correct answer: BD is a shared edge.

Correct answer: ∴ triangle ABD is congruent to triangle DBC by SSS.