1. Pythagorean Theorem

2. Pythagoras
Pythagoras discovered that right triangles have a very special relationship.
He found that if you square leg A and leg B, then add them together, you get the length of the hypotenuse squared. This can be represented by the formula:

3. Using a2+b2=c2

4. The Right Triangle
Hypotenuse c
Leg a
Leg b
Right angle

5. 1. Square both legs 1 2 3 4 5 6 7 8
4 ft 9 10 11 12 13 14 15 16
3 ft
4ft a 1 2 3 4 5 6
3 ft b 7 8 9

6. 2. Count the total squares1 2 3 4 5 6 7 8
4 ft 9 10 11 12 13 14 15 16
3 ft
4ft 1 2 3
= 25 4 5 6
3 ft 7 8 9

7. 3. Put that number of squares on the hypotenuse2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25
3 ft
4 ft
4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16
= 25

8. Essential Question:
How do I solve for a missing hypotenuse length using the Pythagorean theorem?
Pythagorean Theorem

9. Key Points To solve for a missing hypotenuse:
Step 1: Plug the numbers into the formula
Step 2: Take the square of A & B
Step 3: Add A & B
Step 4: Take the square root
Step 5: Check your work by plugging in your answer

10. Study Questions What is the inverse operation of squaring a number?
What variables represent the legs?

11. Step One
A=6
B=8
C=c
Step one plug the numbers into the formula.

12. Step Two
Step two, take the square of A and B.

13. Step Three
Step three,
add A and B.

14. Step Four
Step four: Take the square root

15. Final Step
The final step is to check your work. Check your work by plugging the answer back into the original formula to make sure the answer is correct.

16. Practice
Find the length of the missing side. c
2.3 cm
5.1 cm

17. Practice Step One: Plug the numbers into the formula
Step Two: Take the square of A and B
Step Three: Add A and B
Step Four: Take the square root

18. Practice a = 15, b = 20, c = ? a = 8, b = 10, c = ?

19. Practice a = 15, b = 20, c = 25 a = 8, b = 10, c = 12.81

20. Practice
Find the length of the missing side.
10 m
6 m

21. Practice Step One: Plug the numbers into the formula
Step Two: Take the square of A and C
Step Three: Isolate b by subtracting 36
Step Four: Take the square root

22. Your turn 1) 2) 3)