Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Vocabulary

Review

HSM11_A1MC_1001_T91350 HSM11_A1MC_1001_T91353HSM11_A1MC_1001_T91352

HSM11_A1MC_1001_T91351

HSM11_A1MC_1001_T91355

12 cm

16 cm

20 cm

Chapter 10 290

10-1 The Pythagorean Theorem

1. Circle each right angle below.

2. Underline the correct word or number to complete each sentence.

A right angle has a measure of 60 / 90 / 180 degrees.

Lines that meet at a right angle are parallel / perpendicular lines.

An angle that measures less than a right angle is called a(n) acute / obtuse angle.

Vocabulary Builder

hypotenuse (noun) hy pah tuh noos

Related Word: leg

Definition: In a right triangle, the longest side is the hypotenuse.

Main Idea: The legs of a right triangle form the right angle. The hypotenuse is across from, or opposite, the right angle.

Use Your Vocabulary

Write T for true or F for false.

3. The hypotenuse is the longest side in a right triangle.

4. The hypotenuse of the triangle at the right has length 12 cm.

5. The legs of a right triangle can be any two of the three sides.

6. One leg of the triangle at the right has length 16 cm.

7. The hypotenuse of the triangle at the right has length 20 cm.

HSM11_A1MC_1001_T91354

leg

leg

hypotenuse

HSM12A1MC_1001_NL.indd 290 3/9/11 3:35:34 PM

Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Problem 1

Words

In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Diagram Algebra

a2 1 b2 5 c2

Theorem The Pythagorean Theorem

HSM11_A1MC_1001_T91356

ac

b

8. The diagram at the right shows the sides of a right triangle with a square along each side. Count the number of square units in each region.

A B C

9. Write a sentence relating the number of square units in regions A and B to the number of square units in region C.

__________________________________________________________

__________________________________________________________

__________________________________________________________ HSM11_A1MC_1001_T91357

A

B

CC

HSM11_A1MC_1001_T91358

291 Lesson 10-1

Finding the Length of a Hypotenuse

Got It? What is the length of the hypotenuse of a right triangle with legs of lengths 9 cm and 12 cm?

10. Use the given information to label the sides of the triangle below.

11. Complete each step to find the length of the hypotenuse.

a2 1 b2 5 Pythagorean Theorem

21

25 c2 Substitute for a and b.

1 144 5 c2 Simplify.

5 c2 Add.

5 c Find the principal square root of each side.

5 c Simplify.

12. The length of the hypotenuse is cm.

HSM12A1MC_1001_NL.indd 291 3/9/11 3:35:31 PM

Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Problem 3

Problem 2

1215

a

hsm11a1se_1001_t01990

Property The Converse of the Pythagorean Theorem

If a triangle has sides of lengths a, b, and c, and a2 1 b2 5 c2, then the triangle is a right triangle with hypotenuse of length c.

Underline the correct words to complete each sentence.

14. A triangle with side lengths 12, 16, and 20 is / is not a right triangle because

122 1 162 is equal / not equal to 202.

15. A triangle with side lengths 9, 11, and 14 is / is not a right triangle because

92 1 112 is equal / not equal to 142.

HSM11_A1MC_1001_T91359

20 mm52 mm

47 mm

HSM11_A1MC_1001_T91361

20 mm47 mm

52 mm

HSM11_A1MC_1001_T91360

47 mm20 mm

52 mm

Chapter 10 292

Finding the Length of a Leg

Got It? What is the side length a in the triangle at the right?

13. The equation is solved below. Write a justification for each step.

a2 1 b2 5 c2

a2 1 122 5 152

a2 1 144 5 225

a2 5 81

"a2 5 !81

a 5 9

Identifying Right Triangles

Got It? Could the lengths 20 mm, 47 mm, and 52 mm be the side lengths of a right triangle? Explain.

16. Suppose the triangle is a right triangle. Circle the correctly labeled triangle.

17. Circle the equation you will use to determine whether the triangle is a right triangle.

202 1 472 0 522 522 1 472 0 202 202 1 522 0 472

HSM12A1MC_1001_NL.indd 292 3/9/11 3:35:25 PM

Cop

yrig

ht ©

by

Pear

son

Educ

atio

n, In

c. o

r its

aff

iliat

es. A

ll Ri

ghts

Res

erve

d.

Now Iget it!

Need toreview

0 2 4 6 8 10

Lesson Check

Math Success

12

13x

293 Lesson 10-1

Check off the vocabulary words that you understand.

hypotenuse converse leg Pythagorean Theorem

Rate how well you can use and apply the Pythagorean Theorem.

Error Analysis A student found the length x in the triangle at the right by solving the equation 122 1 132 5 x2. Describe and correct the student’s error.

20. Circle the equation that correctly relates the sides of the triangle.

122 1 132 5 x2 122 1 x2 5 132 x2 1 132 5 122

21. Describe the student’s error.

_______________________________________________________________________

_______________________________________________________________________

22. Find the length x.

• Do you UNDERSTAND?

18. Simplify your equation from Exercise 17.

19. Underline the correct words to complete the sentence.

The equation is true / false , so the triangle is / is not a right triangle.

HSM12A1MC_1001_NL.indd 293 3/9/11 3:35:21 PM