Pulling a One-Eighty! Vocabularychambleems.dekalb.k12.ga.us/Downloads/G7-SSP-CH10-Triangles.pdf ·...

Chapter 10 Skills Practice • 725

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Pulling a One-Eighty!Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems

VocabularyWrite the term that best completes each statement.

1. The 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. The states that the sum of the measures of the interior

angles of a triangle is 180°.

3. The 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. The are the two angles that are

non-adjacent to the specified exterior angle.

Problem SetDetermine the measure of the unknown angle in each triangle.

1.

A

B

C78° 37°

2. P80˚ 66˚

Q

R

m/B 5 180° 2 (78° 1 37°) 5 65°

Lesson 10.1 Skills Practice

Name _______________________________________________________Date _________________________

726 • Chapter 10 Skills Practice

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Lesson 10.1 Skills Practice page 2

3. 35˚

28˚

K

LM

4.

90˚ 32˚

F E

G

5.

60˚

60˚

W

X

Y

6.

110˚

35˚

T

V U

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

7.a

b

c

48°

21°

A

B

C 8.

60˚ 54˚

S

T

r t

s R

m/C 5 180° 2 (48° 1 21°) 5 111°

The shortest side of a triangle

is opposite the smallest angle.

So, the side lengths from shortest

to longest are a, b, c.


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Name _______________________________________________________Date _________________________

9.

28˚118˚

M

K

L

k

l

m

10.

42˚

84˚

Z

YX

yx

z

11.

64˚

79˚67˚

27˚

X Y

W Ze

dca

b 12.

50˚

30˚

60˚90˚

A

u

v

s

r

D

CB

t


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

13.

WX

Y

Z

14.

R S

UT

Interior angles: /XYZ, /YZX, /ZXY

Exterior angle: /WXZ

Remote interior angles: /XYZ, /YZX

15.

E

F

G H

16. B

C

A

D

17. L

MKJ

18.

Q

P

SR


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Name _______________________________________________________Date _________________________

Solve for x in each diagram.

19.

F

Gx

H

J

K

130°

99°

20. V

S

TU

R 140˚

132˚

x

m/GFH 5 180° 2 130° 5 50°

m/GHK 5 m/GFH 1 m/FGH

99° 5 50° 1 x

49° 5 x

21.

H

I

JK

81˚

x2x

22.

R T V S

U

64˚

90˚ (x + 8)


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23.

132˚

112˚

(2x + 4)

K

L

J

N

M

24.

90˚

(3x + 2) (2x + 18)

F

G

D E

Compare the angles in each triangle and determine the unknown information.

25.

S

RQ

T 26.

S

Q

R

P

m/ QRT .m/RST m/PQR m/QRS

m/ RTS , m/QRT m/QSR , m/


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Name _______________________________________________________Date _________________________

27. T

U

VW

28. J

F G H

m/TUV m/UWV m/ m/GHJ

m/WVU m/TUV m/GJH m/FGJ

29. K L M

N

30.

D

C

A B

m/LMN m/KLN m/ABC m/BCD

m/LNM m/KLN m/BAC , m/


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Triangle Construction IConstructing Triangles

Problem SetDetermine whether each combination of given sides and/or angles determines a unique triangle.

1. You are given three angles.

No.

2. You are given three sides.

3. You are given two sides and the included angle.

4. You are given two angles and a side not specified.

5. You are given two angles.

6. You are given two sides.


Name _______________________________________________________Date _________________________


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Construct each triangle using the given sides and/or angles.

7. Construct PQR using the three line segments shown.

Q R

P R

P Q

P R

Q

8. Construct UVW using the three line segments shown.

U

U

W

W

V

V



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9. Construct DEF using the three line segments shown.

D F

ED

E F

10. Construct MNP using the three line segments shown.

M P

PN

M N


Name _______________________________________________________Date _________________________


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11. Construct HJK using the three line segments shown.

H K

KJ

H J

12. Construct ABC using the two line segments and included angle shown.

A B

A

A

C


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Name _______________________________________________________Date _________________________

13. Construct PQR using the two line segments and included angle shown.

P

P

P R

Q

14. Construct DEF using the two line segments and included angle shown.

D E

E

E

F


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15. Construct KMN using the two line segments and included angle shown.

K M

M

M

N

16. Construct WXZ using the two line segments and included angle shown.

W

W

W

Z

X


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Triangle Construction IICongruent Figures and Constructing Congruent Triangles

VocabularyDefine each term in your own words.

1. geometric figures

2. congruent geometric figures

3. corresponding sides

4. corresponding angles

5. included angle

6. included side


Name _______________________________________________________Date _________________________


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Problem SetUse measuring tools to determine whether the given figures are congruent. If the figures are congruent,

then identify and list the corresponding sides and angles. If the figures are not congruent, explain why

they are not.

1. A

D

B

C

E

H

F

G

The figures are congruent.

___

AB > ___

FE , ___

BC > ___

EH , ___

CD > ____

HG , ___

AD > ___

FG , /A > /F, /B > /E, /C > /H, and /D > /G

2. J K

N

P

S

Q

RM


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Name _______________________________________________________Date _________________________

3. B C

D Z

W X

YA

4. D E

FB C

A


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5. M

N

K

G

H

J

6.

Q

R

S

T

U

P


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Name _______________________________________________________Date _________________________

Construct each triangle using the given sides and/or angles.

7. Three sides are given.

a b

c

c

ab


f

e

d


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h

g k

10. Two sides and the included angle are given.

b

a


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Name _______________________________________________________Date _________________________


c d


e

f


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Name _______________________________________________________Date _________________________

14. Two angles and the included side are given.

h

Use the congruence symbol to show the corresponding sides and angles that are congruent based on

each congruence statement.

15. MAT > JEF

___

MA > __

JE , ___

AT > ___

EF , ___

MT > __

JF , /M > /J,

/A > /E, /T > /F

17. CAT > DOG

19. PQR > XYZ

16. LMN > GHJ

18. ABC > KTV

20. DEF > RST


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Pasta Anyone?Triangle Inequality Theorem

VocabularyUse the given figure to complete the statement.

1. According to the Triangle Inequality Theorem, 1 . AC.

A C

B

Problem SetWithout measuring the angles, list the angles of each triangle in order from least to greatest measure.

1.

F

G

H8 in.

9 in.

11 in.

2.

X W

Y

4.7 cm3.6 cm

2.1 cm

The smallest angle of a triangle is

opposite the shortest side. So, the

angles from least to greatest

are /H, /F, /G.


Name _______________________________________________________Date _________________________


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3. Q

RP

8 ft 4 ft

6.43 ft

4. T S

U

9 in

12 in

15 in

5. F

E G6 yd

9.2 yd

4.6 yd

6. K

M

L

4.2 m

5.2 m

5.8 m

Determine whether it is possible to form a triangle using segments with the given measurements.

Explain your reasoning.

7. 3 in., 2.9 in., 5 in. 8. 8 ft, 9 ft, 11 ft

Yes. Because 3 1 2.9 5 5.9, and

5.9 is greater than 5.


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Name _______________________________________________________Date _________________________

9. 4 m, 5.1 m, 12.5 m 10. 7.4 cm, 8.1 cm, 9.8 cm

11. 10 yd, 5 yd, 21 yd 12. 13.8 km, 6.3 km, 7.5 km

13. 112 mm, 300 mm, 190 mm 14. 20.2 in., 11 in., 8.2 in.

15. 30 cm, 12 cm, 17 cm 16. 8 ft, 8 ft, 8 ft


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Write an inequality that expresses the possible lengths of the unknown side of the given triangle.

17. What could be the length of ___

AB ? 18. What could be the length of ___

DE ?

A

10 m

B 8 m C

D

6 cm

F 9 cm E

AB , AC 1 BC

AB , 10 m 1 8 m

AB , 18 m

AC , AB 1 BC

AC 2 BC , AB

10 m 2 8 m , AB

2 m , AB

2 m , AB , 18 m


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Name _______________________________________________________Date _________________________

19. What could be the length of ___

HI ? 20. What could be the length of ___

JL ?

I

20 in.

H 14 in. G

J

12 ft

K 7 ft L


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21. What could be the length of ____

MN ? 22. What could be the length of ___

QR ?

M

3 cm

N 11 cm O

P

9 mm 13 mm

R Q

Pulling a One-Eighty! Vocabularychambleems.dekalb.k12.ga.us/Downloads/G7-SSP-CH10-Triangles.pdf ·...

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