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

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

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

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

Solving Equations with a radical Solve for a 3.) a2 = 60 a = 60 a = 2 15, or -2 15

Solving Equations with a radical Solve for a 4.) a2 = 80 a = 80 a = 4 5 , or -4 5

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

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

Areas of 3 squares 3 X 3 4 X 4 5 X 5

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

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.

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.

Pythagorean Theorem Area = 25 Area =16 9 + 16 = 25 Area = 9

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

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

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

Pythagorean Theorem What did you find????

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

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

Find c if a2 + b2 = c2 1.) a=6, b= 8 2.) 82+152=c2

1.) Find the Hypotenuse a2 + b2 = c2 62 + 82 = c2 36 + 64 = c2 100 = c2 10 = c

2.) Find the Hypotenuse a2 + b2 = c2 82 + 152 = c2 64 + 225 = c2 289 = c2 17 = c

Find c if a2 + b2 = c2 3.) a=12,b=16 4.) 72+242=c2 Now you do these

3.) Find the Hypotenuse a2 + b2 = c2 122 + 162 = c2 144 + 256 = c2 400 = c2 20 = c

4.) Find the Hypotenuse a2 + b2 = c2 72 + 242 = c2 49 + 576 = c2 625 = c2 25 = c

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

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.

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

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

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.) Find a a2 + b2 = c2 a2 + 82 = 102 a2 + 64 = 100 a2 = 36 a = 6

2.) Find a a2 + b2 = c2 a2 + 162 = 202 a2 + 256 = 400 a2 = 144 a = 12

3.) Find a a2 + b2 = c2 a2 + 152 = 172 a2 + 225 = 289 a2 = 64 a = 8

4.) Find a a2 + b2 = c2 a2 + 242 = 252 a2 + 576 = 625 a2 = 49 a = 7

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

Expression with radicals Evaluate b2 - 4ac When a =1, b= -2, c=-3 (-2)2 - 4(1)(-3) 4 + 12 = 16 = 4

Expression with radicals Evaluate b2 - 4ac When a =4, b= 5, c=1 (5)2 - 4(4)(1) 25 - 17 9 = 3 Your Turn

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