Download A n sw e rs 6–6 6–5

© Glencoe/McGraw-Hill
NAME
6–5
DATE
PERIOD
6–6
Enrichment
NAME
DATE
Traceable Figures
The Pythagorean Theorem
Try to trace over each of the figures below without tracing the
same segment twice.
In a right triangle, the square of the hypotenuse, c, is equal to the
sum of the squares of the lengths of the other two sides, a and b.
B
A
K
J
P
PERIOD
Study Guide
c2
52
52
25
L
Q
a2 ! b2
32 ! 42
9 ! 16
25
M
C
Example: How long must a ladder be to reach a window
13 feet above ground? For the sake of stability,
the ladder must be placed 5 feet away from the
base of the wall.
The figure at the left cannot be traced, but the one at the right
can. The rule is that a figure is traceable if it has no points, or
exactly two points where an odd number of segments meet. The
figure at the left has three segments meeting at each of the four
corners. However, the figure at the right has exactly two points,
L and Q, where an odd number of segments meet.
A14
yes, E
D
5
2.
E
P
3
A
2. How long must the brace be on a
closet rod holder if the vertical side is
17 cm and the horizontal side must be
attached 30 cm from the wall?
84.9 ft
V
B
Geometry: Concepts and Applications
2
3.
S
6
E
F
yes, X
W
8
9
X
5
3
4
Y
10
4.
A
© Glencoe/McGraw-Hill
B
yes, D
C
7 3
12 8
3. If Briny is 32 miles due east of Oxford
and Myers is 21 miles due south of
Oxford, how far is the shortest
distance from Myers to Briny?
4. In a baseball game, how far must the
shortstop (halfway between second
base and third base) throw to make an
out at first base? 100.6 ft
2
1
D
11
2
1
11
34.5 cm
R
13
H
1. In a softball game, how far must the
catcher throw to second base?
no
U
C
4
1
7
Solve. Round decimal answers to the nearest tenth.
T
6
(13)2 ! (5)2
169 ! 25
194
w9
w4
w or about 13.9 ft
Ï1
G
E
9
10
H
F
6
5
K
4
38.3 mi
J
G
247
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
248
Geometry: Concepts and Applications
(Lessons 6-5 and 6-6)
c2
c2
c2
c2
Determine whether each figure can be traced. If it can, then
name the starting point and number the sides in the order in
which they should be traced. Sample answers are given.
1.
Answers
D
© Glencoe/McGraw-Hill
NAME
6–6
DATE
PERIOD
Skills Practice
Find the missing measure in each right triangle. Round to the nearest tenth, if necessary.
2.
PERIOD
If c is the measure of the hypotenuse, find each missing measure.
Round to the nearest tenth, if necessary.
3.
c in.
10 in.
4 cm
DATE
Practice
The Pythagorean Theorem
The Pythagorean Theorem
1.
NAME
6–6
33 ft
20 ft
c cm
1. a
8, b
13, c
3. a
Ï1
w3
w,w b
? 15.3
2. a
4, c
6, b
4. b
Ï5
w2
w, c
? 4.5
25 in.
b ft
3 cm
5
4.
26.9
26.2
5.
8 in.
b in.
9 in.
28 m
am
? 5
Ï1
w0
w1
w, a
? 7
Find the missing measure in each right triangle. Round to the
nearest tenth, if necessary.
am
6.
Ï1
w2
w, c
5.
5
6.
10.6
7.
7.2
8.
17.9
9.
7.5
10.
2.8
11.
34
12.
25
3m
4.5 m
4.1
26.2
7.
8.
3.4
9.
25 m
24 ft
6 ft
c in.
3 in.
am
A15
b ft
29 m
Answers
10 m
5 in.
14.7
23.2
Find each missing measure if c is the measure of the hypotenuse. Round to the
nearest tenth, if necessary.
11. b 6, c 10, a ? 8
10. a 15, b 10, c ? 18.0
Geometry: Concepts and Applications
12. c
100, b
14. a
2, b
3, c
60, a
16. b
7, c
15, a
?
80
3.6
?
13.3
?
13. c
16, a
15. c
5, b
17. c
30, a
9, b
2, a
20, b
13.2
?
4.6
?
22.4
?
The lengths of three sides of a triangle are given. Determine whether each triangle is
a right triangle.
18. 3 cm, 4 cm, 5 cm yes
19. 1 ft, 1 ft, 2 ft no
20. 2 in., 2 in., 4 in.
no
22. 5 in., 10 in., 15 in.
21. 8 m, 15 m, 17 m
no
yes
23. 14 cm, 48 cm, 50 cm
yes
The lengths of three sides of a triangle are given. Determine
whether each triangle is a right triangle.
13. 14 ft, 48 ft, 50 ft
yes
15. 15 cm, 36 cm, 39 cm
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249
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
14. 50 yd, 75 yd, 85 yd
yes
no
16. 45 mm, 60 mm, 80 mm
250
no
Geometry: Concepts and Applications
(Lesson 6-6)
5.8