📐 Geometry · Similarity and Right Triangles
The Pythagorean Theorem cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The theorem
- a2 + b2 = c2
- a and b are the legs (they meet at the right angle)
- c is the hypotenuse: across from the right angle, always the longest side
Find the missing side
- Hypotenuse unknown: c = √(a2 + b2)
- Leg unknown: b = √(c2 − a2)
- Check: hypotenuse is longer than each leg and shorter than the sum of the legs
Radicals and decimals
- Pull out the largest perfect square: √180 = 6√5
- Exact: 6√5. Decimal: ≈ 13.42
- Round once, at the end
Is it a right triangle?
- The longest side is c
- Compare a2 + b2 with c2
- Equal: right triangle. Not equal: not a right triangle
Triples
- 3-4-5, 5-12-13, 8-15-17
- Multiply all three numbers by the same whole number for more
- Most right triangles are not triples
Watch out
- Do not call a leg the hypotenuse
- Square, add, then take the square root
- Missing leg: subtract
- Right triangles only
Formulas
- Pythagorean theorem: a2 + b2 = c2
- Hypotenuse: c = √(a2 + b2)
- Missing leg: b = √(c2 − a2)
- Converse test: a2 + b2 = c2, with c the longest side, means a right triangle
- Multiples of a triple: (ka)2 + (kb)2 = (kc)2
The Pythagorean Theorem cheat sheet from HighSchoolQ.com, for personal study use.