Chapter 18: Transformations, congruence and similarity

The chapter problem: enlarge a mural design

A school mural uses a triangular tile with corners at $(1,1)$, $(3,1)$ and $(1,2)$. The designer wants a larger copy, then a smaller reversed copy.

First contact: predict which corner will be farthest from the origin after enlargement by scale factor $2$. You do not need to calculate yet.

Progress checks will help you track how transformations move the tile and how scale factors change its measurements. The Review resolves both copies.

By the end of this chapter you will be able to:

• reflect, rotate, translate and enlarge shapes on a coordinate grid;
• use fractional and negative scale factors;
• prove triangles congruent using valid criteria;
• find missing lengths in similar shapes;
• relate length, area and volume scale factors.

Where it is used

A designer may resize a pattern for a wall, a map, a model or a printed page. The same ideas compare shapes without measuring every side.

Your turn to connect it

Where might you or someone you know resize a design, map or model? Write one example and say which measurement would need to change.

Roadmap

1. 18.1 Reflection, rotation and translation
2. 18.2 Enlargement
3. 18.3 Fractional and negative scale factors
4. 18.4 Congruence criteria
5. 18.5 Similarity and lengths
6. 18.6 Similarity, areas and volumes
7. Review