Special Right Triangles
Section: GeometryBank code: GEO-SPTGRE frequency: HighPro
1. Core Idea
Two right triangles appear so often that their side ratios should be automatic:
- 45-45-90 (half a square): sides in the ratio
1 : 1 : sqrt(2) - 30-60-90 (half an equilateral triangle): sides in the ratio
1 : sqrt(3) : 2
Recognising them means you never need Pythagoras for these shapes — and, crucially, you get an exact answer with a radical rather than a decimal.
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