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Lesson 3-2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 3 11 Glencoe Geometry

3-2Study Guide and InterventionAngles and Parallel Lines

Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal, the following pairs of angles are congruent.

• corresponding angles

• alternate interior angles

• alternate exterior angles

Also, consecutive interior angles are supplementary.

In the figure, m?2 = 75. Find the measures

of the remaining angles. m

1 = 105 ?1 and ?2 form a linear pair.

m

3 = 105 ?3 and ?2 form a linear pair.

m

4 = 75 ?4 and ?2 are vertical angles.

m

5 = 105 ?5 and ?3 are alternate interior angles.

m 6 =

75 ?6 and ?2 are corresponding angles.

m

7 = 105 ?7 and ?3 are corresponding angles.

m

8 = 75 ?8 and ?6 are vertical angles.Exercises

In the figure,

m

3 = 102. Find the measure of each angle.

Tell which postulate(s) or theorem(s) you used.

1. ?5 2. ?6

3. ?11 4. ?7

5. ?15 6. ?14

In the figure,

m

9 = 80 and m?5 = 68. Find the measure

of each angle. Tell which postulate(s) or theorem(s) you used.

7. ?12 8. ?1

9. ?4 10. ?3

11. ?7 12. ?16pq

m n12 34
65
78910
1112
1413
1516
pm n 12 34
65
78wvp
q 12 34
6 5 7 8910
1112
14 13 15 16

Example

102; Alt. Int. Angles Th.78; Cons. Int.

102; Corre. Angles Th. 102; Corre. Angles Th.

102; Corre. Angles Th.

78; Cons. Int. Angles Th;Corre. Angles Th.

100; Supp. Angles

80;Corr. Angles

Th.

100; Cons Int. Angles Th.80; Att. Int.Angles Th.

68; Vertical Angles Th.112; Vertical Angles Th; Cons. Interior Angles Th.Angles Th.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 3 12 Glencoe Geometry

3-2Study Guide and Intervention (continued)

Angles and Parallel Lines

Algebra and Angle Measures Algebra can be used to find unknown values in angles formed by a transversal and parallel lines.

If m?1 = 3x + 15, m?2 = 4x - 5, and m?3 = 5y,

find the value of x and y p ? q, so m?1 = m?2 because they are corresponding angles. m?1 = m?2

3x + 15 = 4x - 5

3 x + 15 - 3x = 4x - 5 - 3x

15 = x - 5

15 + 5 = x - 5 + 5

20 = x

pq r s 12 34
r ? s, so m?2 = m?3 because they are corresponding angles. m?2 = m?3

75 = 5y

75
5 5 y 5

15 = y

Exercises

Find the value of the variable(s) in each figure. Explain your reasoni ng. 1. (5x - 5)° 6 y

4)°

4 x

10)°

2. (15x + 30)° 3 y

18)°10x°90°

3. (11x + 4)° 13 y

5)°(

5 y

5)°

5 x 4. (5x - 20)°3x° 2 y 4 y Find the value of the variable(s) in each figure. Explain your reasoni ng. 5. 2 y

°106°x°(

4 z

6)°

6. 2 x

°2y°

90
x

°z°

Example

x = 15; y = 19; use corresponding and supplementary angles x = 11; y = 10; use consecutive interior angles x = 74; y = 37; z = 25; use consecutive interior, corresponding, and supplementary anglesx = 6; y = 24; Use consecutive interior angles x = 10; y = 25; Use consecutive interior and alternate interior angles x = 30; y = 15 ; z = 150 use supplementary, alternate interior, and consecutive interior anglesquotesdbs_dbs10.pdfusesText_16

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