1. Square Roots and Pythagorean Theorem
Chapter 1
Square Roots and Pythagorean Theorem

2. Square Numbers and Area Models
1.1
Square Numbers and Area Models

3. Is every square a rectangle?
What are descriptors of a rectangle?
Is every square a rectangle?
Is every rectangle a square?
4 sides
4 right angles
What are descriptors of a square?
4 equal sides
4 right angles

4. The SQUARE....a special type of rectangle
4cm
4cm
Area = ???
A = l x w

5. Congruent
the SAME

6. INVESTIGATE With a Partner from your table.....
Which of the following areas can be a square?
4 square units square units
6 square units square units
8 square units square units
9 square units
Draw the rectangles on paper….
How many of the above areas were you able to make a square?
What are the side lengths of each square
How are the side lengths and area related?

7. This is called a SQUARE NUMBER
81cm2
What is the length of all the sides?
This is called a SQUARE NUMBER

8. 4 16 4

9. Working Backwards….
A square has an area of 225cm2. How long is each side of the square? ?
225 cm2 ? ? ?

10. Who are the first 3 groups to finish?
With one partner at your table...
List all the square numbers from 1 to 144.
Who are the first 3 groups to 
finish?

11. The area of my head is 196cm. What is the perimeter?

12. Practice Questions
Pages 8-10
#4b* 5c* 9* 11cd*

13. 1.2 Squares and Square Roots

14. How can we find Square Numbers?
FACTORING
1. Factor 16

15. INVESTIGATE Factoring…

16. A number with an odd number of factors is a SQUARE NUMBER!
Squaring
5² = 5 x 5 = 52 = 25
Square Rooting

17. Find the square... 5
5 x 5 25
Find the Square Root 5
5 x 5 25 25

18. 1. Find the square of 6
2. Find the square root of 49

19. 3. What is the square of 9?
4. What is the square root of 9

20. Which of the following are square-able?

21. Which ones are square rootable?
 


22. Practice! 5d* 6c* 7cd* 11ad* 14cd* 15b* 17 Page 15 - 16
Read Carefully!
Page
5d* 6c* 7cd* 11ad* cd* 15b* 17

23. Measuring Line Segments
1.3
Measuring Line Segments

24. INVESTIGATE
Without using a ruler, find the area and the side length of each square.

25. 1.

26. 2. What are the side lengths of these squares?

27. Questions..
Pages 20-21
3af* bde* ac* 7c* 8b 10a

28. 1.4 Estimating Square Roots

29. From last class…What is the side length?

30. INVESTIGATE 2 11 18 5 24 NO CALCULATORS!
1) Place each square root on the number line below
2) Write the estimated square root as a decimal
NO CALCULATORS!

31. Estimating the square root of a decimal
84.5
84.5 is between which two perfect squares?
____ and _____

32. Example 1.
How can we estimate? 29
It is between ___ & ___
Which means it’s between what two whole numbers?
___ & ___

33. Example 2.
Which whole number is closest to?

34. Example 3.

35. top of the previous layer is 2 cm less in side
Example 4.
This is a four layered
wedding cake. The area
of the bottom cake is
324cm². If the cake on
top of the previous layer
is 2 cm less in side
length, what is the area
of the top layer?

36. 4cd* 5bd* 6(Just Estimate)
Work on your roots...
Page
4cd* 5bd* 6(Just Estimate)
9c* 10b* 13c 16

37. 1.5
The Pythagorean Theorem

38. INVESTIGATE
Make an equation using these symbols. The answer must be 10

39. The “Right” Triangle ?
What does 
this mean?

40. His theorem was....
a² + b² = c² c a b

41. C is ALWAYS the Hypotenuse
A & B are interchangeable

42. What is the length of the hypotenuse?
Example 1.
What is the length of the hypotenuse?
6 cm
7cm

43. Example 2.
What is the height of the triangle?

44. Example 3.
The height of this house is 24 feet and the width of the house is 28 feet. What is the length of one side of the roof?

45. Example 4.

46. Example 5.
How far is the ladder from the wall?
**Which side is c?

47. Practice
Pages
5a*d* 6a*b* 7b*c 8a 13ab
c2 - b2 = a2

48. Exploring the Pythagorean Theorem
1.6
Exploring the Pythagorean Theorem

49. What types of triangles are these?
Do you think we can use the theorem for all of these triangles?

50. INVESTIGATE
Record your results as follows…
What do we notice?

53. Are the following triangles right triangles? 
How do we know?
Example 1) 7cm, 7cm, 81cm
Example 2) 7cm, 24cm, 25cm

54. When three numbers satisfy the Pythagorean Theorem, these numbers are called...
PYTHAGOREAN TRIPLES

55. Which of these sets of numbers is a Pythagorean Triple?
Example 3.
8, 15, 18
Example 4.
11,60, 61

56. Practice
Page
3a*b 6a*d*g* 7f* d

57. 1.7
Applying the Pythagorean Theorem

58. REVIEW from last class... 6 12 Are 8,15,17 Pythagorean Triples?
What is the length of the unknown side? 6 12
Are 8,15,17 Pythagorean Triples?

59. Example 1.

60. Example 2.

61. Example 3.
How long is this line?

62. Example 4. A sloped mountain road is 13 km long.
It covers a horizontal distance of 9 km.
What is the change in elevation of the road?
Give your answer to one decimal place.

63. Example 5.
In shop class, you make a table.  The sides of the table measure 36" and 18". 
If the diagonal of the table measures 43", is the table “square”? 

64. Example 6
What is the width?

65. Practice
Pages 49-51
5b* 6* 8a*b*