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This pdf includes the following topics:-

Identify Complements and Supplements

Adjacent angles

Identify Adjacent Angles

Measures of Complements and Supplements

Congruent Complements Theorem

Congruent Supplements Theorem

Exercises

Identify Complements and Supplements

Adjacent angles

Identify Adjacent Angles

Measures of Complements and Supplements

Congruent Complements Theorem

Congruent Supplements Theorem

Exercises

1.
Page 1 of 7

2.3 Complementary and

Supplementary Angles

Goal Two angles are complementary angles if the sum of their measures

Find measures of is 908. Each angle is the complement of the other.

complementary and

supplementary angles. A

aA and aB are complementary angles.

Key Words 328 588 maA 1 maB 5 328 1 588 5 908

• complementary angles B

• supplementary angles

• adjacent angles Two angles are supplementary angles if the sum of their measures is

• theorem 1808. Each angle is the supplement of the other.

1348 aC and aD are supplementary angles.

468 maC 1 maD 5 1348 1 468 5 1808

C D

EXAMPLE 1 Identify Complements and Supplements

Visualize It! Determine whether the angles are complementary, supplementary,

or neither.

2 a1 and a2 are

1 complementary. a. 228 b. c.

1588

3 158 858

558

a3 and a4 are 358

supplementary. 4

Solution

a. Because 228 1 1588 5 1808, the angles are supplementary.

Complementary angles

make up the Corner of b. Because 158 1 858 5 1008, the angles are neither complementary

a piece of paper.

Supplementary angles nor supplementary.

make up the Side of a

c. Because 558 1 358 5 908, the angles are complementary.

piece of paper.

Identify Complements and Supplements

Determine whether the angles are complementary, supplementary,

or neither.

1. 2. 3.

308

1488

418

398

498 328

2.3 Complementary and Supplementary Angles 67

2.3 Complementary and

Supplementary Angles

Goal Two angles are complementary angles if the sum of their measures

Find measures of is 908. Each angle is the complement of the other.

complementary and

supplementary angles. A

aA and aB are complementary angles.

Key Words 328 588 maA 1 maB 5 328 1 588 5 908

• complementary angles B

• supplementary angles

• adjacent angles Two angles are supplementary angles if the sum of their measures is

• theorem 1808. Each angle is the supplement of the other.

1348 aC and aD are supplementary angles.

468 maC 1 maD 5 1348 1 468 5 1808

C D

EXAMPLE 1 Identify Complements and Supplements

Visualize It! Determine whether the angles are complementary, supplementary,

or neither.

2 a1 and a2 are

1 complementary. a. 228 b. c.

1588

3 158 858

558

a3 and a4 are 358

supplementary. 4

Solution

a. Because 228 1 1588 5 1808, the angles are supplementary.

Complementary angles

make up the Corner of b. Because 158 1 858 5 1008, the angles are neither complementary

a piece of paper.

Supplementary angles nor supplementary.

make up the Side of a

c. Because 558 1 358 5 908, the angles are complementary.

piece of paper.

Identify Complements and Supplements

Determine whether the angles are complementary, supplementary,

or neither.

1. 2. 3.

308

1488

418

398

498 328

2.3 Complementary and Supplementary Angles 67

2.
Page 2 of 7

Student Help Two angles are adjacent angles if they share a common vertex and

side, but have no common interior points.

STUDY TIP

You can use numbers

to refer to angles. common side

Make sure that you

do not confuse angle a1 and a2 are adjacent angles.

names with angle 1 2

measures. common vertex

EXAMPLE 2 Identify Adjacent Angles

Tell whether the numbered angles are adjacent or nonadjacent.

a. b. c.

2

1

5

3 6

4

Solution

a. Because the angles do not share a common vertex or side, a1 and a2

are nonadjacent.

b. Because the angles share a common vertex and side, and they do

not have any common interior points, a3 and a4 are adjacent.

c. Although a5 and a6 share a common vertex, they do not share a

common side. Therefore, a5 and a6 are nonadjacent.

EXAMPLE 3 Measures of Complements and Supplements

a. aA is a complement of aC, and maA 5 478. Find maC.

b. aP is a supplement of aR, and maR 5 368. Find maP.

Solution

a. aA and aC are complements, b. aP and aR are supplements,

so their sum is 908. so their sum is 1808.

maA 1 maC 5 908 maP 1 maR 5 1808

478 1 maC 5 908 maP 1 368 5 1808

478 1 maC 2 478 5 908 2 478 maP 1 368 2 368 5 1808 2 368

maC 5 438 maP 5 1448

Measures of Complements and Supplements

4. aB is a complement of aD, and maD 5 798. Find maB.

5. aG is a supplement of aH, and maG 5 1158. Find maH.

68 Chapter 2 Segments and Angles

Student Help Two angles are adjacent angles if they share a common vertex and

side, but have no common interior points.

STUDY TIP

You can use numbers

to refer to angles. common side

Make sure that you

do not confuse angle a1 and a2 are adjacent angles.

names with angle 1 2

measures. common vertex

EXAMPLE 2 Identify Adjacent Angles

Tell whether the numbered angles are adjacent or nonadjacent.

a. b. c.

2

1

5

3 6

4

Solution

a. Because the angles do not share a common vertex or side, a1 and a2

are nonadjacent.

b. Because the angles share a common vertex and side, and they do

not have any common interior points, a3 and a4 are adjacent.

c. Although a5 and a6 share a common vertex, they do not share a

common side. Therefore, a5 and a6 are nonadjacent.

EXAMPLE 3 Measures of Complements and Supplements

a. aA is a complement of aC, and maA 5 478. Find maC.

b. aP is a supplement of aR, and maR 5 368. Find maP.

Solution

a. aA and aC are complements, b. aP and aR are supplements,

so their sum is 908. so their sum is 1808.

maA 1 maC 5 908 maP 1 maR 5 1808

478 1 maC 5 908 maP 1 368 5 1808

478 1 maC 2 478 5 908 2 478 maP 1 368 2 368 5 1808 2 368

maC 5 438 maP 5 1448

Measures of Complements and Supplements

4. aB is a complement of aD, and maD 5 798. Find maB.

5. aG is a supplement of aH, and maG 5 1158. Find maH.

68 Chapter 2 Segments and Angles

3.
Page 3 of 7

A theorem is a true statement that follows from other true

statements. The two theorems that follow are about complementary

and supplementary angles.

Student Help THEOREMS 2.1 and 2.2

VISUAL STRATEGY

Draw examples of 2.1 Congruent Complements Theorem

these theorems with Words If two angles are complementary

specific measures, as

to the same angle, then they are

shown on p. 52. 3

congruent. 2

1

Symbols If ma1 1 ma2 5 908 and ma2 1 ma3 5 908,

then a1 c a3.

2.2 Congruent Supplements Theorem

Words If two angles are supplementary

5

to the same angle, then they are

congruent. 4 6

Symbols If ma4 1 ma5 5 1808 and ma5 1 ma6 5 1808,

then a4 c a6.

You can use theorems in your reasoning about geometry, as shown in

Example 4.

EXAMPLE 4 Use a Theorem

a7 and a8 are supplementary, and a8 and

8

a9 are supplementary. Name a pair of 7 9

congruent angles. Explain your reasoning.

Solution

a7 and a9 are both supplementary to a8. So, by the Congruent

Supplements Theorem, a7 c a9.

Use a Theorem

6. In the diagram, ma10 1 ma11 5 908, and ma11 1 ma12 5 908.

Name a pair of congruent angles.

Explain your reasoning.

10 11

12

2.3 Complementary and Supplementary Angles 69

A theorem is a true statement that follows from other true

statements. The two theorems that follow are about complementary

and supplementary angles.

Student Help THEOREMS 2.1 and 2.2

VISUAL STRATEGY

Draw examples of 2.1 Congruent Complements Theorem

these theorems with Words If two angles are complementary

specific measures, as

to the same angle, then they are

shown on p. 52. 3

congruent. 2

1

Symbols If ma1 1 ma2 5 908 and ma2 1 ma3 5 908,

then a1 c a3.

2.2 Congruent Supplements Theorem

Words If two angles are supplementary

5

to the same angle, then they are

congruent. 4 6

Symbols If ma4 1 ma5 5 1808 and ma5 1 ma6 5 1808,

then a4 c a6.

You can use theorems in your reasoning about geometry, as shown in

Example 4.

EXAMPLE 4 Use a Theorem

a7 and a8 are supplementary, and a8 and

8

a9 are supplementary. Name a pair of 7 9

congruent angles. Explain your reasoning.

Solution

a7 and a9 are both supplementary to a8. So, by the Congruent

Supplements Theorem, a7 c a9.

Use a Theorem

6. In the diagram, ma10 1 ma11 5 908, and ma11 1 ma12 5 908.

Name a pair of congruent angles.

Explain your reasoning.

10 11

12

2.3 Complementary and Supplementary Angles 69

4.
Page 4 of 7

2.3 Exercises

Guided Practice

Vocabulary Check 1. Explain the difference between complementary angles and

supplementary angles.

2. Complete the statement: Two angles are __?__ if they share

a common vertex and a common side, but have no common

interior points.

Skill Check In Exercises 3–5, determine whether the angles are complementary,

supplementary, or neither. Also tell whether the angles are adjacent

or nonadjacent.

3. 4. 908 5.

308

758

1108 1508

158

6. aA is a complement of aB, and maA 5 108. Find maB.

7. aC is a supplement of aD, and maD 5 1098. Find maC.

Practice and Applications

Extra Practice Identifying Angles Determine whether the angles are

See p. 677. complementary, supplementary, or neither. Also tell whether the

angles are adjacent or nonadjacent.

8. 9. 10.

678

588 318 788 1028

338

Identifying Angles Determine whether the two angles shown on the

clock faces are complementary, supplementary, or neither.

11. 12.

Homework Help

Example 1: Exs. 8–14,

30–32 13. 14.

Example 2: Exs. 8–10

Example 3: Exs. 15–28

33, 34

Example 4: Exs. 38–42

70 Chapter 2 Segments and Angles

2.3 Exercises

Guided Practice

Vocabulary Check 1. Explain the difference between complementary angles and

supplementary angles.

2. Complete the statement: Two angles are __?__ if they share

a common vertex and a common side, but have no common

interior points.

Skill Check In Exercises 3–5, determine whether the angles are complementary,

supplementary, or neither. Also tell whether the angles are adjacent

or nonadjacent.

3. 4. 908 5.

308

758

1108 1508

158

6. aA is a complement of aB, and maA 5 108. Find maB.

7. aC is a supplement of aD, and maD 5 1098. Find maC.

Practice and Applications

Extra Practice Identifying Angles Determine whether the angles are

See p. 677. complementary, supplementary, or neither. Also tell whether the

angles are adjacent or nonadjacent.

8. 9. 10.

678

588 318 788 1028

338

Identifying Angles Determine whether the two angles shown on the

clock faces are complementary, supplementary, or neither.

11. 12.

Homework Help

Example 1: Exs. 8–14,

30–32 13. 14.

Example 2: Exs. 8–10

Example 3: Exs. 15–28

33, 34

Example 4: Exs. 38–42

70 Chapter 2 Segments and Angles

5.
Page 5 of 7

Finding Complements Find the measure of a complement of the

angle given.

15. 16. 17.

868

248

418

18. aK is a complement of aL, and maK 5 748. Find maL.

19. aP is a complement of aQ, and maP 5 98. Find maQ.

Finding Supplements Find the measure of a supplement of the

angle given.

20. 21. 22.

558 1608

148

23. aA is a supplement of aB, and maA 5 968. Find maB.

24. aP is a supplement of aQ, and maP 5 78. Find maQ.

Finding Complements and Supplements Find the measures of a

complement and a supplement of the angle.

25. maA 5 398 26. maB 5 898 27. maC 5 548

Careers

28. Bridges The Alamillo Bridge in Seville, Spain, was designed by

Santiago Calatrava. In the bridge, ma1 5 588, and ma2 5 248.

Find the measures of the supplements of both a1 and a2.

ARCHITECT Santiago

Calatrava, a Spanish born

architect, has developed 1 2

designs for bridges, train

stations, stadiums, and art

Career Links Naming Angles In the diagram, aQPR is a right angle.

CLASSZONE.COM

29. Name a straight angle.

R S

30. Name two congruent supplementary angles.

31. Name two supplementary angles that are

not congruent. P P T

32. Name two complementary angles.

2.3 Complementary and Supplementary Angles 71

Finding Complements Find the measure of a complement of the

angle given.

15. 16. 17.

868

248

418

18. aK is a complement of aL, and maK 5 748. Find maL.

19. aP is a complement of aQ, and maP 5 98. Find maQ.

Finding Supplements Find the measure of a supplement of the

angle given.

20. 21. 22.

558 1608

148

23. aA is a supplement of aB, and maA 5 968. Find maB.

24. aP is a supplement of aQ, and maP 5 78. Find maQ.

Finding Complements and Supplements Find the measures of a

complement and a supplement of the angle.

25. maA 5 398 26. maB 5 898 27. maC 5 548

Careers

28. Bridges The Alamillo Bridge in Seville, Spain, was designed by

Santiago Calatrava. In the bridge, ma1 5 588, and ma2 5 248.

Find the measures of the supplements of both a1 and a2.

ARCHITECT Santiago

Calatrava, a Spanish born

architect, has developed 1 2

designs for bridges, train

stations, stadiums, and art

Career Links Naming Angles In the diagram, aQPR is a right angle.

CLASSZONE.COM

29. Name a straight angle.

R S

30. Name two congruent supplementary angles.

31. Name two supplementary angles that are

not congruent. P P T

32. Name two complementary angles.

2.3 Complementary and Supplementary Angles 71

6.
Page 6 of 7

Beach Chairs Adjustable beach chairs form angles that are

supplementary. Find the value of x.

33. 34.

1168

x8 1408

x8

IStudent Help Using Algebra aABD and aDBC are complementary angles. Find

ICLASSZONE.COM the value of the variable.

HOMEWORK HELP 35. 36. 37.

A B

Extra help with problem A (3k 1 10)8 C

D 5x 8 D

solving in Exs. 35–37 is 13x 8

at classzone.com 8n8

7n8 D 2k8

C

B C A B

38. Complementary Angles aABD and aDBE

D

are complements, and aCBE and aDBE E

are complements. Can you show that

aABD c aCBE? Explain. A

B C

39. Technology Use geometry

software to draw two intersecting

lines. Measure three of the four A C

angles formed. Drag the points P

and observe the angle measures. D

What theorem does this illustrate? B

Complements and Supplements Find the angle measure described.

40. a1 and a2 are both supplementary to a3, and ma1 5 438. Find

the measure of a2.

41. a4 and a6 are both complementary to a5, and ma5 5 858. Find

the measure of a4.

42. aP is supplementary to aQ, aR is supplementary to aP, and

maQ 5 608. Find the measure of aR.

43. Challenge aC and aD are supplementary angles. The measure of

aD is eight times the measure of aC. Find maC and maD.

72 Chapter 2 Segments and Angles

Beach Chairs Adjustable beach chairs form angles that are

supplementary. Find the value of x.

33. 34.

1168

x8 1408

x8

IStudent Help Using Algebra aABD and aDBC are complementary angles. Find

ICLASSZONE.COM the value of the variable.

HOMEWORK HELP 35. 36. 37.

A B

Extra help with problem A (3k 1 10)8 C

D 5x 8 D

solving in Exs. 35–37 is 13x 8

at classzone.com 8n8

7n8 D 2k8

C

B C A B

38. Complementary Angles aABD and aDBE

D

are complements, and aCBE and aDBE E

are complements. Can you show that

aABD c aCBE? Explain. A

B C

39. Technology Use geometry

software to draw two intersecting

lines. Measure three of the four A C

angles formed. Drag the points P

and observe the angle measures. D

What theorem does this illustrate? B

Complements and Supplements Find the angle measure described.

40. a1 and a2 are both supplementary to a3, and ma1 5 438. Find

the measure of a2.

41. a4 and a6 are both complementary to a5, and ma5 5 858. Find

the measure of a4.

42. aP is supplementary to aQ, aR is supplementary to aP, and

maQ 5 608. Find the measure of aR.

43. Challenge aC and aD are supplementary angles. The measure of

aD is eight times the measure of aC. Find maC and maD.

72 Chapter 2 Segments and Angles

7.
Page 7 of 7

Standardized Test 44. Multiple Choice What is the measure of a complement of a

Practice 278 angle?

X

A 538 B 638

X C 1178

X D 1638

X

45. Multiple Choice a1 and a2 are supplementary. Suppose that

ma1 5 608 and ma2 5 (2x 1 20)8. What is the value of x?

X

F 5 G 10

X H 50

X J 100

X

Mixed Review Segment Addition Postulate Find the length. (Lesson 1.5)

46. Find FH. 47. Find KL.

25

F 4.5 G 8.2 H

J 13 K L

&*.

Midpoint Formula Find the coordinates of the midpoint of AB

(Lesson 2.1)

48. A(0, 0), B(8, 2) 49. A(26, 0), B(2, 4) 50. A(4, 1), B(10, 3)

51. A(22, 5), B(22, 7) 52. A(3, 28), B(21, 0) 53. A(25, 29), B(11, 5)

Algebra Skills Evaluating Decimals Evaluate. (Skills Review, p. 655)

54. 2.58 1 8.04 55. 5.17 2 1.96 56. 1.4 3 3.1

57. 0.61 3 0.38 58. 11.2 4 1.4 59. 2 3 5.4 3 3.9

Quiz 1

&.

1. In the diagram, K is the midpoint of JL

Find KL and JL. (Lesson 2.1) J 17 K L

&*. (Lesson 2.1)

Find the coordinates of the midpoint of AB

2. A(1, 3), B(7, 21) 3. A(24, 22), B(6, 4) 4. A(25, 3), B(3, 23)

&*( bisects aJKL. Find the angle measure. (Lesson 2.2)

In Exercises 5–7, KM

5. Find maJKM. 6. Find maJKL. 7. Find maJKL.

K K L

J

M 588

J

118 J

828 M

L

K L M

8. aF is a supplement of aG, and maF 5 1018. Find maG.

(Lesson 2.3)

9. The measure of aD is 838. Find the measure of a complement and

a supplement of aD. (Lesson 2.3)

2.3 Complementary and Supplementary Angles 73

Standardized Test 44. Multiple Choice What is the measure of a complement of a

Practice 278 angle?

X

A 538 B 638

X C 1178

X D 1638

X

45. Multiple Choice a1 and a2 are supplementary. Suppose that

ma1 5 608 and ma2 5 (2x 1 20)8. What is the value of x?

X

F 5 G 10

X H 50

X J 100

X

Mixed Review Segment Addition Postulate Find the length. (Lesson 1.5)

46. Find FH. 47. Find KL.

25

F 4.5 G 8.2 H

J 13 K L

&*.

Midpoint Formula Find the coordinates of the midpoint of AB

(Lesson 2.1)

48. A(0, 0), B(8, 2) 49. A(26, 0), B(2, 4) 50. A(4, 1), B(10, 3)

51. A(22, 5), B(22, 7) 52. A(3, 28), B(21, 0) 53. A(25, 29), B(11, 5)

Algebra Skills Evaluating Decimals Evaluate. (Skills Review, p. 655)

54. 2.58 1 8.04 55. 5.17 2 1.96 56. 1.4 3 3.1

57. 0.61 3 0.38 58. 11.2 4 1.4 59. 2 3 5.4 3 3.9

Quiz 1

&.

1. In the diagram, K is the midpoint of JL

Find KL and JL. (Lesson 2.1) J 17 K L

&*. (Lesson 2.1)

Find the coordinates of the midpoint of AB

2. A(1, 3), B(7, 21) 3. A(24, 22), B(6, 4) 4. A(25, 3), B(3, 23)

&*( bisects aJKL. Find the angle measure. (Lesson 2.2)

In Exercises 5–7, KM

5. Find maJKM. 6. Find maJKL. 7. Find maJKL.

K K L

J

M 588

J

118 J

828 M

L

K L M

8. aF is a supplement of aG, and maF 5 1018. Find maG.

(Lesson 2.3)

9. The measure of aD is 838. Find the measure of a complement and

a supplement of aD. (Lesson 2.3)

2.3 Complementary and Supplementary Angles 73