Pythagorean Theorem (a² + b² = c²) & Right Triangle Geometry
The Pythagorean Theorem is one of the most famous and widely applied mathematical truths in human history. In any right-angled triangle, the area of the square on the hypotenuse (c) is equal to the sum of the areas of the squares on the two legs (a and b).
🧠 Core Mental Strategies & Shortcuts
🔺 Finding the Hypotenuse: c = √(a² + b²)
For legs 3 and 4: c = √(3² + 4²) = √(9 + 16) = √25 = 5.
📐 Finding a Missing Leg: a = √(c² − b²)
For hypotenuse 13 and leg 5: a = √(13² − 5²) = √(169 − 25) = √144 = 12.
⚡ Memorize the Big 4 Pythagorean Triples
Recognizing (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25) lets you solve standardized test questions in 3 seconds.
❓ Frequently Asked Questions
Does the Pythagorean Theorem work on all triangles?
No, it strictly applies to right-angled triangles (triangles with a 90° angle). For non-right triangles, use the Law of Cosines.
Need Classroom Worksheets or Guides?
Explore our complete collection of printable worksheets, step-by-step guides, and interactive calculators.