SAT Math: The Pythagorean Theorem
42+ practice questions in Praczo
The concept, explained
- 1
In a right triangle: a² + b² = c², where c is the hypotenuse (opposite the right angle) and a, b are the legs.
- 2
Common Pythagorean triples to memorize: 3-4-5, 5-12-13, 8-15-17. Any multiple also works (6-8-10, 9-12-15, etc.).
- 3
To find a leg: a² = c² − b². To find the hypotenuse: c = √(a² + b²). Always identify the hypotenuse first.
- 4
For distance between two coordinate points, the horizontal and vertical differences are the legs.
- 5
Converse: if a² + b² = c² the triangle is a right triangle. If a² + b² > c², it's acute. If a² + b² < c², it's obtuse.
- ✗ Adding instead of subtracting when finding a leg: if c = 13 and b = 5, then a² = 13² − 5² = 144, so a = 12, not √(169 + 25).
- ✗ Misidentifying the hypotenuse. It is always the longest side and always opposite the right angle.
SAT-style practice
A ladder leans against a vertical wall. The base of the ladder is 6 feet from the wall, and the ladder reaches 8 feet up the wall. How long is the ladder?
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