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

- 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

- 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

- 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 Ã· Area 2 or Length 1 Ã· Length 2
- Area Scale Factor = (Length S.F.)
^{2}, Volume S.F. = (Length S.F.)^{3}

- 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 Ã· 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.

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