Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Lesson details

      Learning outcome

      I can appreciate and use the criteria by which triangles are congruent (SSS).

      Key learning points

      1. By knowing the three side lengths of the triangle and its image, you can prove congruence.
      2. The corresponding 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.

      Common misconception

      Pupils may believe that as the sides fix the angles, that this implies it is true conversely.

      Use any regular polygon to highlight that the angles will always be the same, but the edge lengths are not always the same length. Regular polygons are always similar but not necessarily congruent.

      Teacher tip

      Have your class, cut two identical sets of four strips of paper and label them a, b, c and d. Get them to investigate how they know for certain that two quadrilaterals are congruent to each other. They can then use only three to look at congruent triangles.

      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

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      In degrees, what is the size of the angle shown?

      An image in a quiz
      Correct Answer: 40, forty

      Q2.
      Select all the quadrilaterals that have at least one pair of equal sides.

      Correct answer: Kite
      Correct answer: Square
      Trapezium
      Irregular quadrilateral
      Correct answer: Parallelogram

      Q3.
      These two rectangles are similar. This means that the side marked $$x$$ is cm.

      An image in a quiz
      Correct Answer: 4, four

      Q4.
      Quadrilaterals ABCD and HEFG are congruent. Match each side or angle in quadrilateral ABCD with a corresponding edge or angle in quadrilateral HEFG.

      An image in a quiz
      Correct Answer:AB,GF
      Correct Answer:CD,EH
      Correct Answer:BC,EF
      Correct Answer:∠DCB,∠FEH
      Correct Answer:∠ADC,∠EHG
      Correct Answer:∠DAB,∠HGF

      Q5.
      A transformation has taken place on a shape. The image is congruent to the object. Which transformation cannot have taken place?

      translation
      reflection
      rotation
      Correct answer: enlargement (SF$$\neq$$1)

      Q6.
      Match each quadrilateral with another quadrilateral that could have the same interior angles.

      Correct Answer:Square,Rectangle
      Correct Answer:Parallelogram,Rhombus
      Correct Answer:Isosceles trapezium,Parallelogram
      Correct Answer:Kite,Trapezium

      6 Questions

      Q1.
      If triangle ABC is congruent to triangle PQR. Match the corresponding equal edges.

      An image in a quiz
      Correct Answer:AB,QR
      Correct Answer:BC,PR
      Correct Answer:AC,QP

      Q2.
      Triangle MNO is congruent to triangle ABC by SSS and MN is 11 cm. Which angle in triangle MNO is opposite MN?

      An image in a quiz
      32°
      45°
      Correct answer: 103°

      Q3.
      Triangle MNO has two angles of 103° and 32°. Side MN is 12 cm. Are triangle ABC and MNO congruent?

      An image in a quiz
      Yes - their corresponding angles are the same.
      Correct answer: No - the corresponding edges are not the same.

      Q4.
      STUV is a square. Match each statement to a reason to prove that triangle STU is congruent to triangle SVU by SSS.

      Correct Answer:ST = SV,as ST and SV are both edges of the same square.
      Correct Answer:TU = VU,as TU and VU are both edges of the same square.
      Correct Answer:SU,is a common edge to both triangles.

      Q5.
      Jun measures each of these triangles. Which of the triangles are congruent to this triangle by SSS?

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

      Q6.
      PQRS is an isosceles trapezium. PR = QS. Match the letters in the proof with the correct edge.

      An image in a quiz
      Correct Answer:a,PQ
      Correct Answer:b,QR
      Correct Answer:c,PR

      To help you plan your 9 maths lesson on: Congruent triangles (SSS), download all teaching resources for free and adapt to suit your pupils' needs...