The Pythagorean Theorem helps us understand the relationship between the sides of a right triangle. The formula is a² + b² = c², where c is the hypotenuse (the longest side) and a and b are the other two sides.
To decide when to add or subtract, let's break it down:
- Identifying the Hypotenuse: If you know two side lengths and need to find the hypotenuse, you'll use addition. For example, if you have sides of 3 and 4, you'd calculate:
- a² + b² = c²: For 3 and 4, that means 3² + 4² = c² → 9 + 16 = c² → 25 = c² → c = 5. Here, we added 9 and 16.
- Working with the Hypotenuse: If you know the hypotenuse and one side, you subtract to find the other side. For example, if you know the hypotenuse is 5 and one side is 4:
- c² = a² + b²: This time, we rearrange it to find the other side: 5² = 4² + b² → 25 = 16 + b².
- Now, subtract 16 from both sides: 25 - 16 = b² → 9 = b² → b = 3. Here, we subtracted.
In summary, remember:
- **Add** when finding the hypotenuse using two sides.
- **Subtract** when finding one side using the hypotenuse and the other side.
Practice with different triangles to get used to knowing when to add or subtract!