Geometry
Pythagorean Theorem
The fundamental relationship in right triangles.
The Formula
a² + b² = c²
Used for: Finding the length of a side in a right triangle
aLength of one leg
bLength of other leg
cHypotenuse (longest side)
🎯 Key Concepts
Understanding the triangle sides:
📐
c is the hypotenuseThe longest side, opposite the 90° angle
🔢
a and b are legsThe two sides that form the right angle
✓
Only for right triangles!This formula only works for 90° triangles
📝 Worked Examples
Find the Hypotenuse
Problem:
a = 3, b = 4. Find c.1
Write formula
a² + b² = c²2
Substitute
3² + 4² = c²3
Calculate
9 + 16 = 25 = c²4
Square root
c = √25 = 5Answer: c = 5
Find a Leg
Problem:
b = 5, c = 13. Find a.1
Rearrange
a² = c² - b²2
Substitute
a² = 13² - 5² = 169 - 253
Calculate
a² = 1444
Square root
a = √144 = 12Answer: a = 12
Is it a Right Triangle?
Problem:
Sides: 5, 12, 13. Right triangle?1
Check
Does 5² + 12² = 13²?2
Calculate
25 + 144 = 169 ✓3
Compare
169 = 169 ✓Answer: Yes! It's a right triangle.
💡 Pro Tips
3-4-5 and friends
Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
Double-check your c
c is ALWAYS the longest side (the hypotenuse)
Real-world use
Used in construction, navigation, and computer graphics