1. Bellwork
5 2
1.) 50
2.) 32
3.) 80
4.) 128
4 2
4 5
8 2

2. Solving Equations with a radical
Solve for a
1.) a2 = 36
2.) a2 = 49
3.) a2 = 60
4.) a2 = 80

3. Solving Equations with a radical
Solve for a
1.) a2 = 36
a = 36
a = 6, or -6

4. Solving Equations with a radical
Solve for a
2.) a2 = 49
a = 49
a = 7, or -7

5. Solving Equations with a radical
Solve for a
3.) a2 = 60
a = 60
a = , or

6. Solving Equations with a radical
Solve for a
4.) a2 = 80
a = 80
a = , or

7. Objective
To be able to use the Pythagorean Theorem to find the lengths of the sides of a Right Triangle.

8. Area of a Square
Area = Length * Width
Length = 4
Width = 4
Area = 16

9. Areas of 3 squares
3 X 3
4 X 4
5 X 5

10. Arrange them into a triangle
5 X 5
4 X 4
3 X 3

11. Now make your squares 1.) 3,4,5 in length Cut out 3 squares that are:
First Draw the Squares on your paper
Cut out 3 squares that are:
1.) 3,4,5 in length
Arrange the sides so they form a Right Triangle.

12. Pythagorean Theorem
In the 3,4,5 triangle add up the areas of the 2 smallest squares and compare that to the area of the largest square.

13. Pythagorean Theorem
Area = 25
Area =16
= 25
Area = 9

14. First Draw the Squares on your paper
Now do #2 and #3.
Now make your squares
First Draw the Squares on your paper
Outline 3 squares that are:
1.) 3,4,5 in length
2.) 6,8,10 in length
3.) 6,7,8 in length

15. Pythagorean Theorem 2.) 6,8,10 in length
Area = 100
Area =36
= 100
Area = 64

16. Pythagorean Theorem 3.) 6,7,8 in length
Area = 64
Area =49
= 64
Area = 36

17. Pythagorean Theorem
What did you find????

18. Pythagorean Theroem a2 + b2 = c2
The sum of the areas of the 2 smaller squares equals the area of the largest square.
This is TRUE for all Right Triangles
a2 + b2 = c2

19. Pythagorean Theorem
Area = c2
Area =a2 c a
a2 + b2 = c2 b
Area = b2

20. Find c if a2 + b2 = c2
1.) a=6, b= 8
2.) =c2

21. 1.) Find the Hypotenuse
a2 + b2 = c2
= c2
= c2
100 = c2
10 = c

22. 2.) Find the Hypotenuse
a2 + b2 = c2
= c2
= c2
289 = c2
17 = c

23. Find c if a2 + b2 = c2
3.) a=12,b=16
4.) =c2
Now you do these

24. 3.) Find the Hypotenuse
a2 + b2 = c2
= c2
= c2
400 = c2
20 = c

25. 4.) Find the Hypotenuse
a2 + b2 = c2
= c2
= c2
625 = c2
25 = c

26. Pythagorean Theorem
What relationship exists between the lengths of the sides of a Right Triangle??

27. Pythagorean Theorem
In a Right Triangle, the sum of the smallest sides squared is equal to the largest side squared.
a2 + b2 = c2 where c is the longest side
The longest side is known as the hypotenuse of the triangle.

28. Pythagorean Theorem a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25 25 = 25
= 25
25 = 25
Where sides (a & b) are the shortest sides and side c is the hypotenuse.

29. a = 6 Find a if b = 8 & c = 10 a2 + b2 = c2 a2 + 82 = 102

30. Find a if a2 + b2 = c2
1.) c=10, b= 8
2.) c=20,b=16
3.) a2+152=172
4.) a2+242=252

31. 1.) Find a
a2 + b2 = c2
a = 102
a = 100
a2 = 36
a = 6

32. 2.) Find a
a2 + b2 = c2
a = 202
a = 400
a2 = 144
a = 12

33. 3.) Find a
a2 + b2 = c2
a = 172
a = 289
a2 = 64
a = 8

34. 4.) Find a
a2 + b2 = c2
a = 252
a = 625
a2 = 49
a = 7

35. Find a if a2 + b2 = c2 1.) c=10, b= 8 1.) a=6 2.) c=20,b=16 2.) a=12

36. Expression with radicals
Evaluate b2 - 4ac When a =1, b= -2, c=-3
(-2)2 - 4(1)(-3)
= = 4

37. Expression with radicals
Evaluate b2 - 4ac When a =4, b= 5, c=1
(5)2 - 4(4)(1)
9 = 3
Your Turn

38. Classwork
Worksheet 9.1
homework:
page 455 (7-34)