Page 4 of 7
4.4 Exercises Guided Practice Vocabulary Check
1. Sketch a right triangle and label its vertices. Then use your
triangle to state the Pythagorean Theorem.
Skill Check
Find the unknown side length. Round your answer to the nearest tenth, if necessary. x
2.
3.
4.
x
x
4
1
8
10
8
2
Find the distance between the points. Round your answer to the nearest tenth, if necessary. 5.
6.
y
y
7.
D (4, 6)
y
B (5, 3)
G (3, 3)
1 1
x
1
A(0, 0)
4
1
C(2, 1)
x 1
F (1, 23)
x
Practice and Applications Extra Practice See p. 681.
Finding a Hypotenuse Find the length of the hypotenuse. 8.
9.
10.
c c
9
c
65
40 9
72
12 11.
12.
24 10
12 8
35
c
15
13.
c
c
Homework Help Example 1: Exs. 8–13, 26 Example 2: Exs. 14–22 Example 3: Exs. 27–34 Example 4: Exs. 27–34
Finding a Leg Find the unknown side length. 14.
25 24
15.
a
16.
b 89
39
5
Ï·· 61 b
4.4 The Pythagorean Theorem and the Distance Formula
195
Page 5 of 7
Pythagorean Triples
EXAMPLE
A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation c 2 5 a 2 1 b 2. For example, the integers 3, 4, and 5 form a Pythagorean triple because 52 5 32 1 42. Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean triple.
c 8 15
Solution (hypotenuse) 2 5 (leg)2 1 (leg)2 2
2
Pythagorean Theorem
2
c 5 8 1 15
Substitute 8 and 15 for the legs.
2
Multiply.
2
Add.
c 5 17
Find the positive square root.
c 5 64 1 225 c 5 289
ANSWER
© Because the side lengths 8, 15, and 17 are integers, they form a Pythagorean triple.
Pythagorean Triples Find the unknown side length. Tell whether the side lengths form a Pythagorean triple. 17.
3
Architecture
18.
b
19.
6
c
7 4
5
c 11
20.
30
16
21.
22.
24
50
9
48 b
c
a
Visualize It! Tell whether the side lengths form a Pythagorean triple. If so, draw a right triangle with the side lengths. 23. 21, 29, 20 PETRONAS TOWERS
These 1483 foot buildings tower over the city of Kuala Lumpur, Malaysia. When the Petronas Towers were designed by Cesar Pelli in 1991, they were the tallest buildings in the world.
shown on page 170 are connected by a skywalk with support beams. Use the diagram to find the approximate length of each support beam.
Application Links
Chapter 4
25. 5, 12, 14
26. Support Beam The skyscrapers
CLASSZONE.COM
196
24. 25, 7, 24
Triangle Relationships
x
x
support beams
Page 6 of 7
Distance Formula Find the distance between the points. Round your answer to the nearest tenth. 27.
28.
y
29.
y
y
F (5, 5)
B (5, 2) D (6, 8)
1 1
x
1 2
A(2, 22)
C(0, 2)
E(4, 21)
2
ICLASSZONE.COM
HOMEWORK HELP Extra help with problem solving in Exs. 30–32 is at classzone.com
Congruence Graph P, Q, and R. Then use the Distance Formula to &* c QR &*. decide whether PQ 30. P(4, 24)
31. P(21, 26)
Q(1, 26) R(21, 23)
32. P(5, 1)
Q(28, 5) R(3, 22)
Q(25, 27) R(23, 6)
Sum of Distances In Exercises 33 and 34, use the map below. Sidewalks around the edge of a campus quadrangle connect the buildings. Students sometimes take shortcuts by walking across the grass along the pathways shown. The coordinate system shown is measured in yards. dorm
dorm
F (0, 30)
B (65, 30)
E (100, 30) dorm
library
IStudent Help
5 x
x
C (0, 15)
A(50, 0)
G (0, 0)
D (100, 0) dorm
classroom
dorm
33. Find the distances from A to B, from B to C, and from C to A if you
have to walk around the quadrangle along the sidewalks. 34. Find the distances from A to B, from B to C, and from C to A if you
are able to walk across the grass along the pathways. Challenge Find the value of x. Use a calculator, and round your answer to the nearest tenth. 35.
36.
37.
x
x
10
6
5
x
3 11
8
8
12
4.4 The Pythagorean Theorem and the Distance Formula
197
Page 7 of 7
Standardized Test Practice
38. Multiple Choice What is the distance from (3, 5) to (21, 24)? A Ï5 w X
B X
Ï1 w7 w
C 2Ï1 w3 w X
D Ï9 w7 w X
39. Multiple Choice Which of the following is the length of the
hypotenuse of a right triangle with legs of lengths 33 and 56? F 65 X
Mixed Review
G X
72.9
H 85.8 X
J 89 X
Finding Absolute Values Evaluate. (Skills Review, p. 662) 40.
27
41.
1.05
42.
0
43.
20.02
Solving Inequalities Solve the inequality. (Algebra Review, p. 167) 44. x 1 5 < 8
Algebra Skills
45. 10 1 x ≥ 12
46. 4x ≥ 28
47. 6x 1 11 ≤ 11
Fractions and Decimals Write the decimal as a fraction in simplest form. (Skills Review, p. 657) 48. 0.4
49. 0.08
50. 0.54
51. 0.12
52. 0.250
53. 0.173
54. 0.3 xx
55. 0.1 xx
Quiz 2 Find the value of x. (Lesson 4.3) 1.
2.
13
3x 2 5
3.
x15
558 (2x 1 1)8
4x 2 16
In Exercises 4–6, find the distance between the points. (Lesson 4.4) 4.
5.
y
6.
y
y
1
A(22, 3)
A(23, 21) 1
B (1, 2) 1
x
1
B (1, 22) 1 B (3, 0) x
1
A(21, 21)
7. A device used to measure windspeed is
attached to the top of a pole. Support wires are attached to the pole 5 feet above the ground. Each support wire is 6 feet long. About how far from the base of the pole is each wire attached to the ground? (Lesson 4.4)
198
Chapter 4
Triangle Relationships
6 ft
5 ft
x
