Sides in the same ratio
No angle is marked here. The three sides alone can decide.
The side-side-side test
Divide each side of one triangle by its matching side. Each answer is a side ratio. Comparing all three side ratios is the side-side-side test, or SSS.
Two triangles are similar if all three side ratios match. Pair the longest with the longest, and the shortest with the shortest.
Pair the sides correctly
Sort the six sides before you divide. Take 4, 5, 6 and 10, 12.5, 15.
| Small side | Large side | Ratio |
|---|---|---|
| 4 | 10 | 2.5 |
| 5 | 12.5 | 2.5 |
| 6 | 15 | 2.5 |
Check: 10 ÷ 4 = 2.5, 12.5 ÷ 5 = 2.5 and 15 ÷ 6 = 2.5. Every ratio is 2.5. The triangles are similar.
For similar triangles, the scale factor also finds a missing side. One pair, 10 and 4, gives 2.5. Then the side matching 5 is 5 × 2.5 = 12.5.
Sort six pairs of triangles.
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