1. 10.3 and 10.4 Pythagorean Theorem

2. c 2 = a 2 + b 2 Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. b a c
c 2 = a 2 + b 2

3. (hypotenuse)2 = (leg)2 + (leg)2
Finding the Length of a Hypotenuse 12 x 5
Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean triple.
SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2
Pythagorean Theorem
x 2 =
Substitute
x 2 =
Multiply.
x 2 = 169
Add.
x = 13
Find the positive square root.
Because the side lengths 5, 12, and 13 are integers, they form a Pythagorean triple.

4. Find the unknown side length.5 ? 3

5. Finding the Length of a Leg
Many right triangles have side lengths that do not form a Pythagorean triple. x 14 7
Find the length of the leg of the right triangle.
SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2
Pythagorean Theorem
14 2 = x 2
Substitute.
196 = 49 + x 2
Multiply.
147 = x 2
Subtract 49 from each side.
147 = x
Find the positive square root.
49 • = x
Use product property.
= x
Simplify the radical.

6. Find the unknown side length.11 14 ?

7. Find the unknown side length.? 1

8. w
W² =
W = √ 250
W = 5 √10

11. Converse of Pythagorean Theorem
If a²+b²=c² , then the triangle is a right triangle

13. Distance between two points
(5,3) -3 5 3 -3
(-3,-3)

14. Find the distance between (0,4) and (-4,-2)

15. Find the distance between (-6,-3) and (6,2)

16. Assignment RPJ: Page 278 (1-7) RPJ: Page 282 (1-9)