The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It is represented by the equation A^2 + B^2 = C^2, where C is the hypotenuse and A and B are the legs. The distance formula calculates the distance between two points in a plane by taking the square root of the sum of the squared differences of their x- and y-coordinates. It is written as √(x2 - x1)2 + (y2 - y1)2. An example of each is provided to demonstrate their use.

1. Pythagorean Theorem and Distance Formula Laverne Thomas

3. A^2 stand for the legs on the triangle

4. B^2 also stand for the legs on the triangle

5. Always use a Right Triangle for Theorem

7. 12^2 + 9 ^2= X^2

8. 144 + 81= X^2

9. 225= X^2

10. X=15 12 9 X

12. Distance Formula Example 10, 16 and 1, 5 X^2 Y^2 X^1 Y^1 X^2 – X^1 + Y^2 – Y^1 (10-1) + (16- 5) 9^2 + 11^2 81 + 121 =202 14.2