3-2 Study Guide and Intervention - Georgetown ISD
NAME
DATE
3-2
PERIOD
Study Guide and Intervention Angles 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. Example In the figure, m∠2 = 75. Find the measures of the remaining angles. = = = = = = =
105 105 75 105 75 105 75
∠1 ∠3 ∠4 ∠5 ∠6 ∠7 ∠8
and and and and and and and
∠2 ∠2 ∠2 ∠3 ∠2 ∠3 ∠6
1 2 4 3
m
5 6 8 7
n
p
Exercises Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
p
form a linear pair. form a linear pair. are vertical angles. are alternate interior angles. are corresponding angles. are corresponding angles. are vertical angles.
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
Lesson 3-2
m∠1 m∠3 m∠4 m∠5 m∠6 m∠7 m∠8
q
1 2 4 3
9 10 12 11
5 6 8 7
m
13 14 16 15
n
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 9. ∠4
8. ∠1 10. ∠3
1 2 4 3 5 6 87
w 11. ∠7
Chapter 3
9 10 12 11
p
13 14 16 15
q
v
12. ∠16
11
Glencoe Geometry
NAME
DATE
3-2
PERIOD
Study 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. Example
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 3x + 15 - 3x = 4x - 5 - 3x 15 = x - 5 15 + 5 = x - 5 + 5
p
q 1
r s, so m∠2 = m∠3 because they are corresponding angles.
2 4
r 3
s
m∠2 = m∠3 75 = 5y 5y 5
75 − =− 5
15 = y
20 = x
Exercises Find the value of the variable(s) in each figure. Explain your reasoning. 1.
2.
(15x + 30)°
(3y + 18)°
10x°
(4x + 10)°
3.
(11x + 4)°
(5y + 5)°
4.
(13y - 5)°
5x°
2y°
3x°
4y°
(5x - 20)°
Find the value of the variable(s) in each figure. Explain your reasoning. 6.
5.
2y° (4z + 6)°
z°
2x° 90° x°
x° 106° 2y°
Chapter 3
12
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(5x - 5)° (6y - 4)°
90°
DATE
3-2
PERIOD
Study Guide and Intervention Angles 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. Example In the figure, m∠2 = 75. Find the measures of the remaining angles. = = = = = = =
105 105 75 105 75 105 75
∠1 ∠3 ∠4 ∠5 ∠6 ∠7 ∠8
and and and and and and and
∠2 ∠2 ∠2 ∠3 ∠2 ∠3 ∠6
1 2 4 3
m
5 6 8 7
n
p
Exercises Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
p
form a linear pair. form a linear pair. are vertical angles. are alternate interior angles. are corresponding angles. are corresponding angles. are vertical angles.
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
Lesson 3-2
m∠1 m∠3 m∠4 m∠5 m∠6 m∠7 m∠8
q
1 2 4 3
9 10 12 11
5 6 8 7
m
13 14 16 15
n
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 9. ∠4
8. ∠1 10. ∠3
1 2 4 3 5 6 87
w 11. ∠7
Chapter 3
9 10 12 11
p
13 14 16 15
q
v
12. ∠16
11
Glencoe Geometry
NAME
DATE
3-2
PERIOD
Study 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. Example
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 3x + 15 - 3x = 4x - 5 - 3x 15 = x - 5 15 + 5 = x - 5 + 5
p
q 1
r s, so m∠2 = m∠3 because they are corresponding angles.
2 4
r 3
s
m∠2 = m∠3 75 = 5y 5y 5
75 − =− 5
15 = y
20 = x
Exercises Find the value of the variable(s) in each figure. Explain your reasoning. 1.
2.
(15x + 30)°
(3y + 18)°
10x°
(4x + 10)°
3.
(11x + 4)°
(5y + 5)°
4.
(13y - 5)°
5x°
2y°
3x°
4y°
(5x - 20)°
Find the value of the variable(s) in each figure. Explain your reasoning. 6.
5.
2y° (4z + 6)°
z°
2x° 90° x°
x° 106° 2y°
Chapter 3
12
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(5x - 5)° (6y - 4)°
90°
