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Checking and securing understanding of congruent triangles (SSS)
I can understand and use the criteria by which triangles are congruent (SSS).
Lesson 3 of 11
New
New
- Year 10
Checking and securing understanding of congruent triangles (SSS)
I can understand and use the criteria by which triangles are congruent (SSS).
Lesson details
Key learning points
- 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.
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.
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.
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 (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.__________ is the multiplier between similar shapes that describes how large one shape is compared to the other.
__________ 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 scale factor
A vector
Q2.This sector is enlarged by scale factor $$\frac{1}{3}$$. The angle in the image is °.
This sector is enlarged by scale factor $$\frac{1}{3}$$. The angle in the image is °.
Correct Answer: 60
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.
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
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.
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
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?
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
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.
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
70, 70 cm
Assessment exit quiz
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.
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
reflection
Correct answer: rotation
rotation
similarity
transformation
Q2.Which of these pairs of shapes look like they are congruent to each other?
Which of these pairs of shapes look like they are congruent to each other?
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q3.Some Oak pupils are discussing congruence. Which pupils are correct?
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."
Andeep: "All squares are similar to each other."
Correct answer: Jun: "All equilateral triangles are similar to each other."
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."
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.
The diagram shows a pair of congruent triangles. The length of the side marked $$x$$ is m.
Correct Answer: 7, seven
7, seven
Q5.The diagram shows a pair of congruent triangles. Which of these Oak pupils are making a correct statement?
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."
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."
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."
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 = 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.
BD is a shared edge.
Correct answer: ∴ triangle ABD is congruent to triangle DBC by SSS.
∴ triangle ABD is congruent to triangle DBC by SSS.
