Congruence and Similarity

Congruence

Similar Lengths

Similar Areas

Similar Volumes

Problems with Similar Shapes

Revising Simlar Lengths

Problems with Similar Shapes

Prerequisite Knowledge

• Use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
• Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; 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 the 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.