The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. An example calculates the length of the hypotenuse of a triangle with sides of lengths 10 and 6 units. The distance formula calculates the distance between two points in the xy-plane by taking the square root of the sum of the squared differences of the x- and y-coordinates, as shown in an example finding the distance between points (1,4) and (10,16).

1. Pythagorean theorem and distance formulaReshawn Whaley

2. Pythagorean theoremPythagorean Theorem is the lengths of the three sides in a right angle.The variables are a2 + b2 = c2The type of triangle we use is a right triangle.

3. Pythagorean Theorem Examplea2+ b2 = c2102 + 62 = c2100 + 36 = 136Square Root of 136 is 11.6106

4. Distance formulaDistance formula is the formula that allows you to find the distance between two points in the xy-plane. The steps you use to solve distance formula is (x2 – x1)2 + (y2 – y1)2 = c2.

5. Distance Formula Example(1,4) (10,16)(10-1)2 + (16-4)292 + 122 = 225Square root of 225 is 15.