Congruence and Similarity

Scheme of work: GCSE Higher: Year 10: Term 2: Congruence and Similarity

Prerequisite Knowledge

  • Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
  • Know and apply formulae to calculate: the area of triangles, parallelograms, and trapezia; the volume of cuboids and other right prisms (including cylinders)
  • Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement

Success Criteria

  • Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures.
  • Compare lengths, areas and volumes using ratio notation; make links to similarity and scale factors

Key Concepts

  • Similar shapes have equal angles, whereas congruent shapes have equal angles and lengths.
  • Students need to be able to use ratios in form 1 : n to model the length scale factor.
  • To calculate the correct scale factor students need to match corresponding dimensions, e.g., Area 1 ÷ Area 2 or Length 1 ÷ Length 2
  • Area Scale Factor = (Length S.F.)2, Volume S.F. = (Length S.F.)3

Common Misconceptions

  • Students often struggle with proving congruence. Encourage them to annotate sketch diagrams with clearly marked angles and state the angle properties used.
  • Scale factors are can be incorrectly calculated using different measures, e.g., Area ÷ Length
  • The incorrect scale factor can be applied to calculate an unknown dimension. For instance, students may use the Area scale factor to find a length.

Congruence and Similarity Resources

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