NAME _____________________________________________ DATE ____________________________ PERIOD ____________

Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 83

Lesson 5 Homework Practice

The Pythagorean Theorem

Write an equation you could use to find the length of the missing side of each right triangle.

Then find the missing length. Round to the nearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. a, 65 cm; c, 95 cm 8. a, 16 yd; b, 22 yd

Determine whether each triangle with sides of given lengths is a right triangle.

Justify your answer.

9. 18 ft, 23 ft, 29 ft 10. 7 yd, 24 yd, 25 yd

11. The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. Find the length

of the other leg.

12. A leg of a right triangle is 30 meters long, and the hypotenuse is 35 meters long. What is the

length of the other leg?

13. TELEVISIONS The diagonal of a television measures 27 inches. If the width of a 27-inch is

22 inches, calculate its height to the nearest inch.

Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 83

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.Lesson 5 Homework PracticeThe Pythagorean Theorem

Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary.

1.

10 ft

b ft

8 ft

2. 26 in.

24 in.

a in.

3. 18 cm

15 cmc cm

4.

14 yd28 yd

a yd 5.

50 mm

50 mm

c mm

6.

45 m

64 m

c m

7. a, 65 cm; c, 95 cm 8. a, 16 yd; b, 22 yd

Determine whether each triangle with sides of given lengths is a right triangle. Justify your answer.

9. 18 ft, 23 ft, 29 ft 10. 7 yd, 24 yd, 25 yd

11. The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. Find the length of the other leg.

12. A leg of a right triangle is 30 meters long, and the hypotenuse is 35 meters long. What is the length of the other leg?

13. TELEVISIONS The diagonal of a television measures 27 inches. If the width of a 27-inch is 22 inches, calculate its height to the nearest inch.

8 2 + b 2 = 102; 6 ft a 2 + 24 2 = 26 2 ; 10 in. 18 2 + 15 2 = c 2 ; 23.4 cm

a 2 + 14 2 = 2 8 2 ; 24.2 yd 5 0 2 + 5 0 2 = c 2 ; 70.7 mm 4 5 2 + 6 4 2 = c 2 ; 78.2 m

6 5 2 + b 2 = 9 5 2 ; 69.3 cm 1 6 2 + 2 2 2 = c 2 ; 27.2 yd

1 8 2 + 2 3 2 = 853 ≠ 2 9 2 7 2 + 2 4 2 = 625 = 2 5 2 no; yes;

about 10.2 in.

about 18.0 m

16 in.

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84 Course 3 • Chapter 5 Triangles and the Pythagorean Theorem

Lesson 5 Problem-Solving Practice

The Pythagorean Theorem

1. ART What is the length of a diagonal of a

rectangular picture whose sides are 12 inches

by 17 inches? Round to the nearest tenth of

an inch.

2. GARDENING Ross has a rectangular

garden in his back yard. He measures one

side of the garden as 22 feet and the

diagonal as 33 feet. What is the length of

the other side of his garden? Round to the

nearest tenth of a foot.

3. TRAVEL Troy drove 8 miles due east and

then 5 miles due north. How far is Troy from

his starting point? Round the answer to the

nearest tenth of a mile.

4. GEOMETRY What is the perimeter of a

right triangle if the hypotenuse is 15

centimeters and one of the legs is 9

centimeters?

5. ART Anna is building a rectangular picture

frame. If the sides of the frame are 20 inches

by 30 inches, what should be the diagonal

measure? Round to the nearest tenth of an

inch.

6. CONSTRUCTION A 20-foot ladder leaning

against a wall is used to reach a window

that is 17 feet above the ground. How far

from the wall is the bottom of the ladder?

Round to the nearest tenth of a foot.

7. CONSTRUCTION A door frame is 80

inches tall and 36 inches wide. What is the

length of a diagonal of the door frame?

Round to the nearest tenth of an inch.

8. TRAVEL Tina measures the distances

between three cities on a map. The

distances between the three cities are 45

miles, 56 miles, and 72 miles. Do the

positions of the three cities form a right

triangle?

84 Course 3 • Chapter 5 Triangles and the Pythagorean Theorem

NAME _____________________________________________ DATE __________________ PERIOD _________

Copyright © The M

cGraw

-Hill Com

panies, Inc. Permission is granted to reproduce for classroom

use.Lesson 5 Problem-Solving PracticeThe Pythagorean Theorem

1. ART What is the length of a diagonal of a rectangular picture whose sides are 12 inches by 17 inches? Round to the nearest tenth of an inch.

2. GARDENING Ross has a rectangular garden in his back yard. He measures one side of the garden as 22 feet and the diagonal as 33 feet. What is the length of the other side of his garden? Round to the nearest tenth of a foot.

3. TRAVEL Troy drove 8 miles due east and then 5 miles due north. How far is Troy from his starting point? Round the answer to the nearest tenth of a mile.

4. GEOMETRY What is the perimeter of a right triangle if the hypotenuse is 15 centimeters and one of the legs is 9 centimeters?

5. ART Anna is building a rectangular picture frame. If the sides of the frame are 20 inches by 30 inches, what should be the diagonal measure? Round to the nearest tenth of an inch.

6. CONSTRUCTION A 20-foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the bottom of the ladder? Round to the nearest tenth of a foot.

7. CONSTRUCTION A door frame is 80 inches tall and 36 inches wide. What is the length of a diagonal of the door frame? Round to the nearest tenth of an inch.

8. TRAVEL Tina measures the distances between three cities on a map. The distances between the three cities are 45 miles, 56 miles, and 72 miles. Do the positions of the three cities form a right triangle?

20.8 in.

24.6 ft

9.4 mi36 cm

10.5 ft36.1 in.

87.7 in.no

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NAME _____________________________________________ DATE ____________________________ PERIOD ____________

Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 37

Enrich

Geometric Relationships

The Pythagorean Theorem can be used to express

relationships between parts of geometric figures. d2 = s

2 + s

2

The example shows how to write a formula for d2 = 2s

2

the length of the diagonal of a square in terms of the d = s

length of the side.

Develop a formula for each problem. The dashed lines have been included to help you.

1. An equilateral triangle has three 2. A regular hexagon has six sides of the

sides of the same length. Express the same length. Express the height h in

altitude h in terms of the side s. terms of the length of the side s.

3. A circle is circumscribed about a 4. A circle is inscribed in a square. Express

square. Express the radius r of the the radius r of the inscribed circle in

circumscribed circle in terms of the terms of the side s of the square.

side s of the square.

5. Use the isosceles triangle below. 6. Use the isosceles right triangle below.

Express the altitude h in terms Express x in terms of s.

of the quantity a.

NAME ________________________________________ DATE _____________ PERIOD _____Multi-Part

Lesson 2BPART

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Course 3 • Triangles and Transformations 37

Geometric RelationshipsThe Pythagorean Theorem can be used to express relationships between parts of geometric figures. d2 = s2 + s2

The example shows how to write a formula for d2 = 2s2

the length of the diagonal of a square in terms of the d = √ � 2 slength of the side.

Develop a formula for each problem. The dashed lines have been included to help you.

1. An equilateral triangle has three 2. A regular hexagon has six sides of thesides of the same length. Express the same length. Express the height h in altitude h in terms of the side s. terms of the length of the side s.

h = √ � 3 s

− 2 s

h

h = √ � 3 s

− 2

3. A circle is circumscribed about a 4. A circle is inscribed in a square. Express square. Express the radius r of the the radius r of the inscribed circle in circumscribed circle in terms of the terms of the side s of the square.side s of the square.

r = s −

√ � 2 or

√ � 2 s −

2 r =

s −

2

5. Use the isosceles triangle below. 6. Use the isosceles right triangle below.Express the altitude h in terms Express x in terms of s.of the quantity a. h = 3a

x = s −

√ � 2 or

√ � 2 s −

2

Enrich

032_043_NACRMC3C08_895178.indd 37 1/5/10 8:26:01 AM

Blizzard Bag Due March 20, 2015

Teacher Name: Veelman

Class Name: 8th

Math

Assignment Information:

Students need to complete a Skills Practice, Problem Solving, and Extra Practice

worksheet for Pythagorean Theorem. This is a review of learning that took place

on this subject recently.

This work covers the following Common Core State Standards and Mathematical

Practices:

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in

right triangles in real-world and mathematical problems in two and

three dimensions.

8.EE.2 Use square root and cube root symbols to represent solutions to

equations of the form x2 = p and x3 = p, where p is a positive rational

number. Evaluate square roots of small perfect squares and cube roots

of small perfect cubes. Know that is irrational.

Mathematical Practices 1, 3, and 4 are aspects of mathematical thinking that are

emphasized in every lesson. Students are given opportunities to be persistent in

their problem solving, to express their reasoning, and apply mathematics to real-

world situations.

*Students can use their book for any help or review since it contains many solid

examples of what Pythagorean Theorem is and how to find missing sides of a right

triangle.

*The assignment will be graded as a homework/class work grade on Progress

Book.

*You will receive a failing grade if this is not completed and turned in on time.

*Please turn in the assignment when finished.