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Year 9

Applying the criteria for congruence

I can identify congruent triangles and prove why they are congruent.

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New
New
Year 9

Applying the criteria for congruence

I can identify congruent triangles and prove why they are congruent.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. If two triangles are congruent, then one of the proven criteria must apply.
  2. By stating the criteria (that you have already proven), you can prove congruence.
  3. It is important to be clear why you know that two triangles are congruent.

Common misconception

Pupils may think they need to know the actual size or length to be able to prove congruence.

Remind pupils that if they can show that the corresponding angles or sides are the same length, then that is all that is needed. For example, if the corresponding edges are both edges of the same regular polygon, then they 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.

You may wish to provide pupils with copies of the diagrams on the slides or a mini-whiteboard to allow them to add to the diagrams any further information that is implied by the properties of the shapes or can be calculated from the given information.
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).

Video

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Starter quiz

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6 Questions

Q1.
In triangle XYZ, angle $$m$$ is °.
An image in a quiz
Correct Answer: 32, thirty two, thirty-two, 32°
Q2.
Select the right-angled triangles. (Diagrams are not drawn accurately)
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Correct Answer: An image in a quiz
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Correct Answer: An image in a quiz
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Correct Answer: An image in a quiz
An image in a quiz
Q3.
The square has a perimeter of 36 cm. The perimeter of the regular hexagon is cm.
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Correct Answer: 54, fifty four
Q4.
All of these triangles are translations, rotations or reflections of each other. If they were cut out you could fit them exactly on of top of each other. You can say the triangles are .
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Correct Answer: congruent
Q5.
The quadrilaterals ABCD and EFGH are congruent and AD = 6 cm. Which edge on EFGH is also 6 cm?
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EF
FG
Correct answer: GH
EH
Q6.
Complete the statement. Triangle ABC and triangle XYZ are ____________.
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congruent as the three interior angles are all the same.
Correct answer: similar as the three interior angles are the same.
neither similar nor congruent.

Exit quiz

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6 Questions

Q1.
Which of the following are criteria for proving two triangles are congruent?
AAA
Correct answer: ASA
Correct answer: SAS
SSA
Correct answer: RHS
Q2.
Triangle ABC and triangle DEF are congruent by __________.
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Correct answer: ASA
RHS
SAS
SSS
Q3.
There is insufficient information to prove triangle ABC is congruent to triangle MNO by __________.
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Correct answer: ASA
RHS
SAS
SSS
Q4.
Triangle KLM is __________ to triangle XYZ.
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definitely congruent
definitely incongruent
Correct answer: potentially congruent
Q5.
If you know that ABCD is a parallelogram, then __________ criteria for congruent triangles (ASA, RHS, SAS and SSS) can be used to show ABD and BDC are congruent.
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0
1
2
3
Correct answer: 4
Q6.
Matching a, b, c and d to the correct statements to complete this congruence proof.
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Correct Answer:a,CD

CD

Correct Answer:b,DE

DE

Correct Answer:c,angle CDF

angle CDF

Correct Answer:d,angle CDE

angle CDE