Triangles

This chapter focuses on similarity rather than congruence. Similar figures have the same shape but may differ in size, and proportional reasoning becomes central here.

Two figures are similar when corresponding angles are equal and corresponding sides are in the same ratio. This idea extends far beyond triangles, but triangles give the cleanest theorems and proofs.

When triangles are similar, a wide set of side ratios and area relations become available. These results are essential in geometry proofs and measurement problems.

The standard criteria are AA, SSS and SAS. Students should not just memorise these names, but understand what information each criterion requires and why it works.