1. Solving Equations with a radical 1.) a2 = 36
2.) a2 = 49
3.) a2 = 60
4.) a2 = 80
2. Solving Equations with a radical 1.) a2 = 36
a = 36
a = 6, or -6
3. Solving Equations with a radical 2.) a2 = 49
a = 49
a = 7, or -7
4. Solving Equations with a radical 3.) a2 = 60
a = 60
a = 2 15, or -2 15
5. Solving Equations with a radical 4.) a2 = 80
a = 80
a = 4 5 , or -4 5
6. Area of a Square Area = Length * Width
7. Areas of 3 squares
8. Arrange them into a triangle
9. Pythagorean Theorem Area =16
10. Now make your squares Outline 3 squares that are:
1.) 3,4,5 in length
11. Pythagorean Theorem 2.) 6,8,10 in length Area =36
12. Pythagorean Theorem 3.) 6,7,8 in length Area =49
13. Pythagorean Theroem The sum of the areas of the 2 smaller squares equals the area of the largest square.
This is TRUE for all Right Triangles
14. Pythagorean Theorem Area =a2
15. Find c if a2 + b2 = c2 1.) a=6, b= 8
2.) 82+152=c2
16. 1.) Find the Hypotenuse a2 + b2 = c2
62 + 82 = c2
36 + 64 = c2
100 = c2
10 = c
17. 2.) Find the Hypotenuse a2 + b2 = c2
82 + 152 = c2
64 + 225 = c2
289 = c2
17 = c
18. Find c if a2 + b2 = c2 3.) a=12,b=16
4.) 72+242=c2
19. 3.) Find the Hypotenuse a2 + b2 = c2
122 + 162 = c2
144 + 256 = c2
400 = c2
20 = c
20. 4.) Find the Hypotenuse a2 + b2 = c2
72 + 242 = c2
49 + 576 = c2
625 = c2
25 = c
21. Pythagorean Theorem What relationship exists between the lengths of the sides of a Right Triangle??
22. 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.
23. Pythagorean Theorem a2 + b2 = c2
32 + 42 = 52
9 + 16 = 25
25 = 25
Where sides (a & b) are the shortest sides and side c is the hypotenuse.
24. Find a if b = 8 & c = 10 a2 + b2 = c2
a2 + 82 = 102
a2 + 64 = 100
a2 + 64 - 64 = 100 - 64
a2 = 36
25. Find a if a2 + b2 = c2 1.) c=10, b= 8
2.) c=20,b=16
3.) a2+152=172
4.) a2+242=252
26. 1.) Find a a2 + b2 = c2
a2 + 82 = 102
a2 + 64 = 100
a2 = 36
a = 6
27. 2.) Find a a2 + b2 = c2
a2 + 162 = 202
a2 + 256 = 400
a2 = 144
a = 12
28. 3.) Find a a2 + b2 = c2
a2 + 152 = 172
a2 + 225 = 289
a2 = 64
a = 8
29. 4.) Find a a2 + b2 = c2
a2 + 242 = 252
a2 + 576 = 625
a2 = 49
a = 7
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 1.) a=6
2.) a=12
3.) a=8
4.) a=7
31. Expression with radicals Evaluate b2 - 4ac When a =1, b= -2, c=-3
(-2)2 - 4(1)(-3)
4 + 12 = 16 = 4
