Similarity

Similarity is a generalisation of congruence: two similar figures have the same shape but not necessarily the same dimensions. If the similarity ratio is $k$, lengths are multiplied by $k$, areas by $k^2$ and volumes by $k^3$. In this chapter we define similar triangles and their fundamental criterion, we derive the scaling laws for lengths, areas and volumes and, by combining similarity with Pythagoras’ theorem, we arrive at Euclid’s theorems on the right-angled triangle.

Sections

• Similar triangles
• Metric relations in the right-angled triangle

Exercises

• All the worked exercises of the chapter