A Pythagorean triple is a set of whole-number sides that already satisfy a² + b² = c². Memorize 3-4-5, 5-12-13, and 8-15-17, plus their multiples. You still need the theorem when the sides are not a triple. That is in the Pythagorean theorem and special right triangles.
The list
3-4-5 and 6-8-10 and 9-12-15 are the same triangle scaled. 5-12-13 and 10-24-26 are the next family. 7-24-25 and 8-15-17 show up less often but save the same square-and-add work. If two sides match a triple, fill in the third without a calculator.
45-45-90 and 30-60-90 are not triples. They use √2 and √3. Keep those on the special-triangle list, not this one. Right-triangle trig that starts from a triple is in SOH-CAH-TOA.
The bottom line
If two sides look like 3-4-5 or 5-12-13, scale and fill in. Otherwise square, add, and take a square root. Formulas are in ACT Math formulas, and triangle questions more broadly are in triangle problems.
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