Pythagorean Theorem Flashcards

Grade 8 · Math · Flashcards

Review the key concepts, formulas, and vocabulary of the Pythagorean Theorem.

Flashcards

Pythagorean Theorem: a² + b² = c² where a and b are legs and c is the hypotenuse of a right triangle.
Hypotenuse: The longest side of a right triangle; opposite the right angle; labeled c.
Legs of a right triangle: The two sides that form the right angle; labeled a and b.
Pythagorean triple: Three whole numbers satisfying a²+b²=c². Examples: 3-4-5, 5-12-13, 8-15-17.
Finding c (hypotenuse): c = √(a² + b²)
Finding a missing leg: a = √(c² − b²) — subtract the known leg² from hypotenuse².
Is it a right triangle?: Yes if a²+b²=c². No if the equation is not satisfied.
Square root (√): The inverse of squaring; √49=7 because 7²=49.
The 3-4-5 triple: 3²+4²=5² (9+16=25). Multiples like 6-8-10 and 9-12-15 also work.
The 5-12-13 triple: 5²+12²=13² (25+144=169).
Real-world uses: Construction (right angles), navigation (shortest path), screen sizes (diagonal).
45-45-90 triangle: Legs are equal; hypotenuse = leg × √2. From the Pythagorean Theorem with a=b.