# 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 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

### Mr Mathematics Blog

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing

#### 3D Vectors – Year 2

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Pure 2: 3D Vectors

#### Parametric Equations

Edexcel A-Level Mathematics Year 2: Pure 2: Parametric Equations