The Pythagorean Theorem is a rule used in right triangles (triangles with a 90° angle).

It helps you find a missing side length of the triangle.

🔺 Right Triangle Parts

In a right triangle:

• The two shorter sides are called the legs
  → usually labeled a and b

• The longest side is called the hypotenuse
  → labeled c
  → it is always across from the 90° angle

⭐ The Formula

a^2 + b^2 = c^2

Meaning:

• square the first leg

• square the second leg

• add them together

• that equals the square of the hypotenuse

🧠 Why it Works (Simple Idea)

The theorem compares the areas of squares built on each side of the triangle:

• A square with side length a has area a^2

• A square with side length b has area b^2

• A square with side length c has area c^2

And in a right triangle:

a^2 + b^2 = c^2

So the two smaller squares’ areas add up to the biggest square’s area.

🧮 Example 1 (Finding the Hypotenuse)

If:

• a = 3

• b = 4

Then:

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

c = 5

So the hypotenuse is 5.

🧮 Example 2 (Finding a Missing Leg)

If:

• c = 13

• a = 5

Then:

5^2 + b^2 = 13^2

25 + b^2 =169

b^2 =144

b = 12

So the missing leg is 12.

⚠️ Important Notes

✅ Only works for right triangles
✅ The hypotenuse is always the longest side
✅ The hypotenuse is always opposite the 90° angle