Math II Teachers Skills Practice Chapter 03

Lesson 3.1

Skills Practice

Name

Date

Inside Out

Triangle Sum, Exterior Angle, and Exterior Angle

Inequality Theorems

Vocabulary

Write the term that best completes each statement.

1. T

 he

Exterior Angle Inequality Theorem

states that the measure of an exterior angle of a

triangle is greater than the measure of either of the remote interior angles of the triangle.

2. T

 he

???

Triangle Sum Theorem

angles of a triangle is 180¡ã.

????

3

states that the sum of the measures of the interior

3. T

 he

??? Exterior Angle Theorem

??? states that the measure of an exterior angle of a

triangle is equal to the sum of the measures of the remote interior angles of the triangle.

4. T

 he

remote interior angles of a triangle

non-adjacent to the specified exterior angle.

are the two angles that are

Problem Set

Determine the measure of the missing angle in each triangle.

1. 

2.

B

P

Q

80¡ã

A

78¡ã

37¡ã

66¡ã

C

? Carnegie Learning

R

mªÐB 5 180¡ã 2 (78¡ã 1 37¡ã) 5 65¡ã m/R 5 180¡ã 2 (80¡ã 1 66¡ã) 5 34¡ã

Chapter 3 Skills Practice

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Lesson 3.1

Skills Practice

3. 

K

page 2

4.

G

35¡ã

28¡ã

M

90¡ã

L

32¡ã

F

E

m/L 5 180¡ã 2 (28¡ã 1 35¡ã) 5 117¡ã m/G 5 180¡ã 2 (90¡ã 1 32¡ã) 5 58¡ã

3

5. W

6.

T

110¡ã

60¡ã

60¡ã

X

35¡ã

V

U

Y

m/Y 5 180¡ã 2 (60¡ã 1 60¡ã) 5 60¡ã m/U 5 180¡ã 2 (110¡ã 1 35¡ã) 5 35¡ã

List the side lengths from shortest to longest for each diagram.

B

8.

C

a

48¡ã

S

b

c

21¡ã

t

r

A

60¡ã

T

440

54¡ã

s

R

m/C 5 180¡ã 2 (48¡ã 1 21¡ã) 5 111¡ã

m/S 5 180¡ã 2 (54¡ã 1 60¡ã) 5 66¡ã

The shortest side of a triangle

is opposite the smallest angle.

So, the side lengths from shortest

to longest are a, b, c.

The shortest side of a triangle

is opposite the smallest angle.

So, the side lengths from shortest

to longest are r, t, s.

Chapter 3 Skills Practice

? Carnegie Learning

7.

Lesson 3.1

Skills Practice

page 3

Name

Date

9.

M

10.

Z

k

l

28¡ã

L

x

42¡ã

118¡ã

m

K

y

84¡ã

X

z

Y

m/M 5 180¡ã 2 (118¡ã 1 28¡ã) 5 34¡ã m/Y 5 180¡ã 2 (84¡ã 1 42¡ã) 5 54¡ã

The shortest side of a triangle

is opposite the smallest angle.

So, the side lengths from shortest

to longest are l, m, k.

11.

X

b

67¡ã

The shortest side of a triangle

is opposite the smallest angle.

So, the side lengths from shortest

to longest are z, y, x.

12.

Y

79¡ã

50¡ã

d

a 27¡ã c

r

30¡ã

60¡ã

e

Z

A

v

t

64¡ã

W

C

u

B

3

s

90¡ã

D

? Carnegie Learning

m/X 5 180¡ã 2 (67¡ã 1 27¡ã) 5 86¡ã m/A 5 180¡ã 2 (60¡ã 1 30¡ã) 5 90¡ã

m/Z 5 180¡ã 2 (64¡ã 1 79¡ã) 5 37¡ã m/C 5 180¡ã 2 (90¡ã 1 50¡ã) 5 40¡ã

The shortest side of a triangle is

opposite the smallest angle. Side c is

the longest side of «±WXY, and the

shortest side of «±WYZ. So, the side

lengths from shortest to longest

are b, a, c, d, e.

The shortest side of a triangle is

opposite the smallest angle. Side t is

the longest side of «±ABD, and the

shortest side of «±BCD. So, the side

lengths from shortest to longest

are s, r, t, v, u.

Chapter 3 Skills Practice

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Lesson 3.1

Skills Practice

page 4

Identify the interior angles, the exterior angle, and the remote interior angles of each triangle.

13.

14.

Y

W

U

T

X

Z

R

S

Interior angles: /XYZ, /YZX, /ZXY Interior angles: /RST, /RTS, /SRT

Exterior angle: /WXZ

Exterior angle: /STU

Remote interior angles: /XYZ, /YZX Remote interior angles: /RST, /SRT

3

15.

16.

F

E

G

B

C

H

A

D

Interior angles: /EFG, /EGF, /FEG Interior angles: /ABC, /ACB, /BAC

Exterior angle: /FGH Exterior angle: /BAD

Remote interior angles: /EFG, /FEG Remote interior angles: /ABC, /ACB

17.

18.

L

P

Q

K

M

R

S

Interior angles: /JKL, /JLK, /KJL Interior angles: /QRS, /QSR, /RQS

Exterior angle: /LKM Exterior angle: /PQS

Remote interior angles: /JLK, /KJL Remote interior angles: /QRS, /QSR

442

Chapter 3 Skills Practice

? Carnegie Learning

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Lesson 3.1

Skills Practice

page 5

Name

Date

Solve for x in each diagram.

19.

20.

G

R

x

x

130¡ã

J

F

H

132¡ã

99¡ã

140¡ã

S

V

T

U

K

m/GFH 5 180¡ã 2 130¡ã 5 50¡ã ?m/RTS 5 180¡ã 2 132¡ã 5 48¡ã

3

m/GHK ?5 m/GFH 1 m/FGH m/RSV 5 m/RTS 1 m/SRT

??? 99¡ã??5 50¡ã 1 x ? ?? 140¡ã 5 48¡ã 1 x

??? 49¡ã??5 x

??92¡ã 5 x

???

21.

22.

I

H

x

U

2x

J 81¡ã

64¡ã

K

(x + 8¡ã)

90¡ã

R

V

T

S

m/IJK 5 180¡ã 2 81¡ã 5 99¡ã ?m/UTV 5 180¡ã 2 90¡ã 5 90¡ã

? Carnegie Learning

m/IJK 5 m/HIJ 1 m/IHJ m/SVU 5 m/UTV 1 m/TUV

?????99¡ã 5 2x 1 x ????x 1 8¡ã 5 90¡ã 1 64¡ã

????99¡ã 5 3x ????x 1 8¡ã 5 154¡ã

????33¡ã 5 x ??

x 5 146¡ã

Chapter 3 Skills Practice

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