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      Applying the criteria for congruence

      Lesson details

      Learning outcome

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

      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.

      Keywords

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

      Teacher tip

      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.

      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.
      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)

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      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.

      An image in a quiz
      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 .

      An image in a quiz
      Correct Answer: congruent

      Q5.
      The quadrilaterals ABCD and EFGH are congruent and AD = 6 cm. Which edge on EFGH is also 6 cm?

      An image in a quiz
      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.

      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 __________.

      An image in a quiz
      Correct answer: ASA
      RHS
      SAS
      SSS

      Q3.
      There is insufficient information to prove triangle ABC is congruent to triangle MNO by __________.

      An image in a quiz
      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.

      An image in a quiz
      0
      1
      2
      3
      Correct answer: 4

      Q6.
      Matching a, b, c and d to the correct statements to complete this congruence proof.

      An image in a quiz
      Correct Answer:a,CD
      Correct Answer:b,DE
      Correct Answer:c,angle CDF
      Correct Answer:d,angle CDE

      To help you plan your 9 maths lesson on: Applying the criteria for congruence, download all teaching resources for free and adapt to suit your pupils' needs...