1. SOL 8.10
Pythagorean Theorem

2. For Right Triangles Only!
What is a right triangle?
A triangle with a 90 degree angle.
Hypotenuse – always opposite the right angle; always the longest side
leg
leg

3. Pythagorean Theorem The Pythagorean Theorem states: a2 + b2 = c2
Hypotenuse (c)
Leg (a)
Leg (b)

4. Example 1 Solve for x. a2 + b2 = c2 62 + 82 = x2 36 + 64 = x2 100 = x2

5. Example 2 Solve for y. a2 + b2 = c2 72 + 42 = y2 49 + 16 = y2 65 = y2

6. Your Turn!
Use the Pythagorean Theorem to solve. Round to the nearest tenth, if necessary.
Legs: 12 and 9 15
Legs: 16 and 12 20
Legs: 100 and 200
223.6

7. To the nearest tenth of a foot, find the length of the diagonal of a rectangle with a width of 4 feet and a length of 10 feet.
a2 + b2 = c2
= x2
= x2
116 = x2
√116 = √x2
x = 10.8 x
4 ft
10 ft

8. Tonight’s Homework! Legs: 4 and 5 Legs: 9 and 5 Legs: 7 and 12
Solve. Round to the nearest tenth, if necessary!
Answers
Legs: 4 and 5
Legs: 9 and 5
Legs: 7 and 12
Legs: 24 and 32
Legs: 15 and 8
Legs: 0.4 and 0.3
Legs: 20 and 21
Legs: 7.2 and 9.6
6.4
10.3
13.9 40 17
0.5 29 12