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      Lesson details

      Learning outcome

      I can recognise that for congruent shapes both side lengths and angle sizes are preserved.

      Key learning points

      1. Two shapes are not congruent if there is a pair of lengths with a scalar not equal to one.
      2. Congruent does not mean the orientation must be the same.
      3. The angle sizes do not change.

      Keywords

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

      • Co-interior angles - Co-interior angles are on the same side of the transversal line and in between the two other lines.

      Common misconception

      Pupils may think that they do not have enough information about a shape to determine whether it is congruent to another shape, when in fact they do.

      Pupils could attempt the draw the shape based on the information that they have. They can then consider whether there are multiple way that the shape can be drawn while still satisfying all the given information.

      Teacher tip

      In Task B, pupils could check whether the shapes they make are congruent by cutting them out and then placing one on top of the other.

      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.
      Which transformations always produce an image that is congruent to the object?

      enlargement
      Correct answer: reflection
      Correct answer: rotation
      Correct answer: translation

      Q2.
      When two shapes are congruent, which property of the shapes always remain invariant?

      Correct answer: angles
      Correct answer: lengths
      orientation
      position

      Q3.
      The table shows the base and height of four rectangles. Which rectangle is congruent to a rectangle that is 6 cm by 3 cm?

      An image in a quiz
      A
      Correct answer: B
      C
      D

      Q4.
      Which triangle is congruent to triangle T?

      An image in a quiz
      A
      Correct answer: B
      C
      D
      E

      Q5.
      Angles in a quadrilateral sum to °.

      Correct Answer: 360, three hundred and sixty, 360°

      Q6.
      The diagram shows a pair of angles on parallel lines. When $$x=145$$, $$y=$$ .

      An image in a quiz
      Correct Answer: 35, thirty five, 35 degrees, 35 deg, 35°

      6 Questions

      Q1.
      Triangles A and B are congruent. Match each unknown length from triangle B with its size.

      An image in a quiz
      Correct Answer:$$a\text{ cm}$$,4 cm

      4 cm

      Correct Answer:$$b\text{ cm}$$,6 cm

      6 cm

      Correct Answer:$$c\text{ cm}$$,5 cm

      5 cm

      Q2.
      Triangles A and B are congruent. Match each unknown angle from triangle B with its size.

      An image in a quiz
      Correct Answer:$$a°$$,44°

      44°

      Correct Answer:$$b°$$,79°

      79°

      Correct Answer:$$c°$$,57°

      57°

      Q3.
      The image shows two congruent hexagons. What is the size of the angle $$x°$$?

      An image in a quiz
      110°
      112°
      Correct answer: 146°

      Q4.
      The image shows two congruent pentagons. What is the value of $$x$$?

      An image in a quiz
      43
      Correct answer: 50
      59

      Q5.
      Shape T is a trapezium. Which quadrilateral contains enough information to determine whether it is congruent to shape T?

      An image in a quiz
      A
      Correct answer: B
      C

      Q6.
      Shape R is a rhombus. Which quadrilateral is not congruent to shape R?

      An image in a quiz
      A
      B
      Correct answer: C

      To help you plan your 9 maths lesson on: Congruence in shapes, download all teaching resources for free and adapt to suit your pupils' needs...