Congruence and Similarity

March 12, 2023

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 Ã· Area 2 or Length 1 Ã· 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 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.

Congruence and Similarity Resources

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