# Congruence and Similarity

Students learn how about the difference between similar and congruent shapes.  Learning progresses from proving congruency and similarity to using different scale factors to calculate an unknown length, area or volume.  This unit takes place in Term 2 of Year 10 and follows on from transformations.

##### Revision Lessons

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.

### Mr Mathematics Blog

#### Trigonometric Identities Sin, Cos and Tan

How to introduce the sin, cos and tan trigonometric identities.

#### Calculating a Reverse Percentage

How to teach calculating the original amount after a percentage change.

#### Comparing Datasets using the Mean and Range

The importance of the range when comparing comparing datasets.