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Lesson 8-2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 8 11 Glencoe Geometry

Study Guide and Intervention

The Pythagorean Theorem and Its Converse

The Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. If the three whole numbers a , b, and c satisfy the equation a2 + b 2 = c 2 , then the numbers a , b, and c form a

Pythagorean triple.

ca b ACB a. Find a. a 1213
ACB a2 + b 2 = c 2

Pythagorean Theorem

a 2 + 12 2 = 13 2 b = 12, c = 13 a 2 + 144 = 169 Simplify. a 2 = 25 Subtract. a = 5 Take the positive square root of each side. b. Find c. c

3020ACB

a 2 + b 2 = c 2

Pythagorean Theorem

20 2 + 30 2 = c 2 a = 20, b = 30

400 + 900 = c

2

Simplify.

1300 = c

2 Add. ⎷ ?? 1300 = c Take the positive square root of each side.

36.1 ≈ c Use a calculator.

Find x.

1. x33 2. x 159
3. x65 25 4.
x 5 9 4 9 5. x 3316
6. x 11

28Use a Pythagorean Triple to find x.

7. 8 17 x 8. 45
24x
9. 28
96x

8-2Example

Exercises

? ABC is a right triangle. so a 2 + b 2 = c 2 1 3

1345≈ 36.7

663≈ 25.7

18 or 3

2 ≈ 4.2 12 60

15 51 100

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 8 12 Glencoe Geometry

ca b AC B

Study Guide and Intervention (continued)

The Pythagorean Theorem and Its Converse

Converse of the Pythagorean Theorem If the sum of the squares of the lengths of the two shorter sides of a triangle equals the square of the lengths of the longest side, then the triangle is a right triangle. You can also use the lengths of sides to classify a triangle. If a 2 + b 2 = c 2 , then if a 2 + b 2 = c 2 then ABC is a right triangle. ?ABC is a right triangle. if a 2 + b 2 > c 2 then ABC is acute. if a 2 + b 2 < c 2 then ABC is obtuse.

Determine whether ?PQR is a right triangle.

a 2 + b 2 ? c 2

Compare c

2 and a 2 + b 2 10 2 + (10 ⎷ ? 3 ) 2 ? 20 2 a = 10, b = 10 ⎷ ? 3 , c = 20

100 + 300 ? 400 Simplify.

400 = 400? Add.

Since c

2 = and a 2 + b 2 , the triangle is a right triangle.

Exercises

Determine whether each set of measures can be the measures of the sides of a triangle. If so, classify the triangle as acute , obtuse, or right. Justify your answer.

1. 30, 40, 50 2. 20, 30, 40 3. 18, 24, 30

4. 6, 8, 9 5. 6, 12, 18 6. 10, 15, 20

7. ⎷ ? 5 , ⎷ ?? 12 , ⎷ ?? 13 8. 2, ⎷ ? 8 , ⎷ ?? 12 9. 9, 40, 41 2010

10⎷3

8-2

Example

yes, right; yes, obtuse; yes, right; 50
2 = 30 2 + 40 2 40
2 > 20 2 + 30 2 30
2 = 24 2 + 18 2 yes, acute; no; 6 + 12 = 18 yes, obtuse; 9 2 < 6 2 + 8 2 20 2 > 10 2 + 15 2 yes, acute; yes, right; yes, right; 13 2 5 2 12 2 12 2 8 2 + 2 2 41
2 = 40 2 + 9 2quotesdbs_dbs5.pdfusesText_9

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