The big picture
Here is the track, one idea per line.
| Idea | Remember | Example |
|---|---|---|
| Similar | Equal angles, sides in one ratio | 3-4-5 and 6-8-10 |
| AA | Two matching angles | 50° and 60° in both |
| SSS | Three side ratios match | 4, 5, 6 and 10, 12.5, 15 |
| SAS | Two ratios and the angle between | 4 and 6, 6 and 9, at 50° |
| Shadows | On flat ground, height ÷ shadow is one ratio | 2 m pole, 8 m tree |
| Parallel line | It splits two sides in one ratio | AD ÷ DB = AE ÷ EC |
| Converse | Equal splits from the same corner mean parallel | 4/6 = 6/9 |
| Corner triangle | ADE is similar to ABC | AD ÷ AB = DE ÷ BC |
| Which test | Match corners, then pick the test | AA, SSS, SAS or none |
This is Chapter 6, Triangles. Open its exercises. In each one, match the corners first.
Most numbers here were chosen to be simple. The tests work for any triangles.