7.1 – Apply the Pythagorean Theorem

Pythagorean Theorem:

leg

leg

hypotenusea

b

c

c2 = a2 + b2

(hypotenuse)2 = (leg)2 + (leg)2

If a triangle is a right triangle, then (hypotenuse)2 = (leg)2 + (leg)2

1. Find the value of x.

c2 = a2 + b2

x2 = 152 + 362

x2 = 225 + 1296

x2 = 1521

x = 39

H

1. Find the value of x.

c2 = a2 + b2

x2 = 42 + 92

x2 = 16 + 81

x2 = 97

97x

H

1. Find the value of x.

c2 = a2 + b2

x2 = 62 + 32

x2 = 36 + 9

x2 = 45

53x

H

1. Find the value of x. c2 = a2 + b2

172 = x2 + 82

289 = x2 + 64

225 = x2

x15

H

1. Find the value of x. c2 = a2 + b2

272 = x2 + 92

729 = x2 + 81

648 = x2

x218H

1. Find the value of x. c2 = a2 + b2

422 = x2 + 362

1764 = x2 + 1296

468 = x2

x136

H

2. Find the area of the isosceles triangle.c2 = a2 + b2

102 = h2 + 82

100 = h2 + 64

36 = h2

x6

8 8

bhA2

1

1(16)(6)

2A

8

48A in2

HH

2. Find the area of the isosceles triangle.c2 = a2 + b2

122 = h2 + 42

144 = h2 + 16

128 = h2

bhA2

1

1(8)(8 2)

2A

4

32 2A

h28

cm2

H

2. Find the area of the isosceles triangle.c2 = a2 + b2

442 = h2 + 242

1936 = h2 + 576

1360 = h2

bhA2

1

1(48)(4 85)

2A

24

96 85A

h854

m2

24 24

H

7.2 – Converse of the Pythagorean

Pythagorean Theorem Converse:

If c2 = a2 + b2, then the triangle is a right triangle

a

b

c

Acute Triangle:

If c2 < a2 + b2, then the triangle is acute

a

b

c

Obtuse Triangle:

If c2 > a2 + b2, then the triangle is obtuse

a

b

c

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

c2 = a2 + b2

172 = 82 + 152

289 = 64 + 225

289 = 289

8 + 15 > 17

8 + 17 > 15

15 + 17 > 8

Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

a. 8, 15, 17

3 + 4 > 9

b. 3, 4, 9

Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

7 > 9

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

c2 = a2 + b2

196 = 100 + 121

196 221

c.

Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

10, 11, 14

10 + 11 > 14

10 + 14 > 11

11 + 14 > 10

142 = 102 + 112

<

c2 = a2 + b2

61 = 25 + 36

61 = 61

d. 2 2 261 5 6

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

5, 6, 61

61 7.8

5 + 6 > 7.8

5 + 7.8 > 6

6 + 7.8 > 5

12 ,10 ,13 c2 = a2 + b2

144 = 13 + 100

144 113

e.

222 101312

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

13 3.6

3.6 + 10 > 12

3.6 + 12 > 10

10 + 12 > 3.6

>

c2 = a2 + b2

37.21 = 18.49 + 27.04

37.21 45.53

f. 4.3, 5.2, 6.1 2 2 26.1 4.3 5.2

For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

4.3 + 5.2 > 6.1

4.3 + 6.1 > 5.2

5.2 + 6.1 > 4.3 <

7.17.2

436-439444-445

3, 5, 13-17 odd, 24, 26, 31, 39, 403-7 odd, 15-21 odd, 25

HW Problem

7.1 #26

Ans:

c2 = a2 + b2

52 = a2 + 32

25 = a2 + 916 = a2

aH H

4 = a

c2 = a2 + b2

x2 = 42 + 72

x2 = 16 + 49x2 = 65

65x