Triangle and Period

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NAME ______________________________________________ DATE

____________ PERIOD _____

7-1

Practice

(Average)

Geometric Mean
Find the geometric mean between each pair of numbers to the nearest tenth. 1. 8 and 12 2. 3 7 and 6 7 3. 4 and 2 5

96

9.8

126

11.2

8 5

1.3

Find the measure of each altitude. State exact answers and answers to the nearest tenth. 4. T U

5. J
V

6

M
17

5 A

12

L

K

Answers

60

7.7

102

10.1

Find x, y, and z. 6.
y
8

7.
23

25

6

x z

z

x

(Lesson 7-1)

y

184 713
8.
y
2 3

13.6; 26.7

248

15.7;

114 475
9.
z

10.7; 21.8

150

12.2;

10

z

x

x

20

y

4.5;

13

3.6; 6.5

15; 5;

300

17.3

10. CIVIL ENGINEERING An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth. 2.88 mi

 

 

©

Glencoe/McGraw-Hill

354

Glencoe Geometry

NAME ______________________________________________ DATE

____________ PERIOD _____

7-2
Find x. 1.
x

Practice

(Average)

The Pythagorean Theorem and Its Converse
2.
23 13 34 21

3.
26

26

x
18

x

698
4.
34

26.4
5.
22

715
x
14

26.7
6.

595
24

24.4
x
42 24

x

16

1640

40.5

60

7.7

135

11.6

Answers

Determine whether

GHI is a right triangle for the given vertices. Explain. 1) 8. G( 6, 2), H(1, 12), I( 2, 1)

7. G(2, 7), H(3, 6), I( 4,

yes; GH

2, HI

98,

no; GH

149, HI 17,
2

130,

IG

(

2)

100,

2

(

98 )

2

(

100 )
4)

IG

2

(

130 )

(

17 )

2

(
9)

149 )

2

(Lesson 7-2)

9. G( 2, 1), H(3,

1), I( 4,

10. G( 2, 4), H(4, 1), I( 1,

yes; GH

29, HI

58,

yes; GH

45, HI

125,

IG

(

29 )

29,

2

(

29 )

2

(

58 )

IG

2

(

45 )

170,

2

(

125 )

2

(

170 )

2

Determine whether each set of measures can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean triple. 11. 9, 40, 41 12. 7, 28, 29 13. 24, 32, 40

yes, yes
14. ,
9 12 ,3 5 5

no, no
15.
1 2 2 , 3 ,1 3

yes, yes
16. 7 ,
4 2 3 4 , 7 7

yes, no
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