2.2 – Angle Relationships and Parallel Lines
Name _____________________________ Per._______
1. Label a pair of the following angles as ∠1 and ∠2.
a. corresponding ∠s
b. alternate exterior ∠s
6. consecutive interior ∠s
d. alternate interior ∠s
2. Classify the angle pair as corresponding, alternate interior, alternate exterior, consecutive interior, linear pair, or
vertical angles.
a) ∠3 and ∠9
b) ∠5 and ∠13
c) ∠4 and ∠10
d) ∠5 and ∠15
e) ∠7 and ∠14
f) ∠1 and ∠11
g) ∠2 and ∠4
h) ∠13 and ∠16
3. Solve for 𝑥. Explain. (hint: you don’t need the parallel lines)
4. ∠𝐽𝐸𝑋 and which of the following angles are known as
alternate interior angles?
J
A. ∠𝑋𝐹𝑆
E
D
K
B. ∠𝐷𝐹𝑋
F
T
C. ∠𝐾𝐹𝐷
X
S
D. ∠𝑆𝐹𝐸
5. Use the diagram below to fill in the blanks.
K
a. ∠𝐿𝑀𝑊 and ∠________ are consecutive interior angles.
L
b. ∠𝐾𝑀𝑈 and ∠________ are alternate exterior angles.
U
M
c. ∠𝑀𝑆𝐺 and ∠________ are corresponding angles.
E
S
G
W
d. ∠𝑊𝑀𝑈and ∠________ are alternate interior angles.
e. ∠𝐺𝑆𝐾and ∠________ are vertical angles.
f. ∠𝑈𝑀𝑊and ∠________ are a linear pair.
6. In the diagram below, ∠𝑃𝑆𝐸 is corresponding angles
with which other angle?
B. ∠𝑇𝐵𝑃
C. ∠𝑀𝑆𝐺
D. ∠𝐺𝐵𝑇
V
P
A. ∠𝑉𝐵𝑆, ∠𝑆𝐵𝑇
P
A. ∠𝑉𝐵𝑆
7. Which set of angles are consecutive interior angles?
T
B
M
S
B. ∠𝐺𝑆𝑀, ∠𝑇𝐵𝑆
E
G
C. ∠𝑃𝑆𝑀, ∠𝑇𝐵𝑆
D. ∠𝑀𝑆𝐵, ∠𝑉𝐵𝐺
V
T
B
M
S
E
G
when lines are parallel…MAGIC!
Label the measures of all the missing angles in the diagram.
8.
9.
10. If ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐶𝐷, are the angle pairs congruent or supplementary? Explain.
E
a. ∠𝐴𝐺𝐸 and ∠𝐹𝐻𝐷
b. ∠𝐴𝐺𝐻 and ∠𝐴𝐻𝐸
c. ∠𝐵𝐺𝐹 and ∠𝐸𝐻𝐶
d. ∠𝐷𝐻𝐹 and ∠𝐵𝐺𝐻
A
G
B
C
H
F
D
For #s 11-16, use the diagram below to find the angle measures. Explain your reasoning
11. If 𝑚∠2 = 120°, what
is 𝑚∠6?
12. If 𝑚∠7 = 122°, what
is 𝑚∠2?
13. If 𝑚∠5 = 56°, what
is 𝑚∠8?
14. If 𝑚∠3 = 118°, what
is 𝑚∠5?
15. If 𝑚∠4 = 51°, what
is 𝑚∠5?
16. If 𝑚∠6 = 130°, what
is 𝑚∠8?
16. Solve for 𝑥. Explain. (hint: you don’t need the parallel lines)
17. In the diagram below, ∠1 ≅ ∠5. Which of the
following conclusions does not have to be true?
a.
b.
c.
d.
𝑚∠3 ≅ 𝑚∠7
𝑚∠3 + 𝑚∠6 = 180 is
𝑚∠4 ≅ 𝑚∠7
𝑎 is parallel to 𝑏
a
1
2
3
4
5
6
7
8
b
18. To solve for x in the diagram below, Alice set up the following equation: −1 + 14𝑥 = 12𝑥 + 17. Which of the
following statements below would justify her reasoning?
A. If two lines are parallel and cut by a transversal, then the corresponding
angles are congruent.
B. If two lines are parallel and cut by a transversal, then the consecutive interior
angles are supplementary.
C. If two lines are parallel and cut by a transversal, then the alternate exterior
angles are congruent.
D. If two lines are parallel and cut by a transversal, then the alternate interior
angles are congruent.
19. Solve for 𝑥. Explain.
20. 𝑔 ∥ ℎ. Solve for 𝑥. Explain.
g
h
(5x +5)°
(9x +21)°
(9x +21)
(9x +21)
(5x +5)
(5x
21.+5)
Write
a proof.
Given: 𝑎 ∥ 𝑏; 𝑚∠2 = 78°
Prove: 𝑚∠1 = 78°
b
a
1
2
Statements
Reasons
22. Write a proof.
Given: 𝑐 ∥ 𝑑; 𝑚∠3 = 63°
Prove: 𝑚∠4 = 117°
Statements
°
c
3
4
Reasons
°
°
°
23. Solve for 𝑥. Explain.
24. Solve for 𝑥. Explain.
25. Write a proof.
Given: 𝑚 = ℎ; ℎ = 𝑝
Prove: 𝑚 = 𝑝
26. Write a proof.
Given: 𝑚 ∥ 𝑛; 𝑚∠5 = 54°
Prove: 𝑚∠6 = 54°
2 step proof!
Statements
27. Write a proof.
Given: 𝑝 ∥ 𝑞; 𝑚∠2 = 114°
Prove: 𝑚∠3 = 66°
Reasons
Statements
1.
2. 𝑚∠1 = 𝑚∠2
3.
5. 𝑚∠2 + 𝑚∠3 = 180°
6.
3
2
p
q
7. 𝑚∠3 = 66°
5
n
Statements
4. 𝑚∠1 + 𝑚∠3 = 180°
1
m
Reasons
Reasons
1.
2.
3. ∥ lines → cons. int. ∠s supp.
4.
5.
6.
7. subtraction property
6
d
Let’s review
29. What is the coordinates of 𝑊′ after a rotation 90°
counterclockwise about the origin?
28. Using a straightedge and a compass, construct the
angle bisector of the angle shown below.
A. (3, 1)
B. (−1. −3)
C. (−3, −1)
D. (1, −3)
30. Given: ̅̅̅̅
𝑅𝐴 bisects ∠𝐶𝐴𝑁;
𝑚∠𝐶𝐴𝑅 = 43°
Prove: 𝑚∠𝑅𝐴𝑁 = 43°
N
R
C
Statements
T
̅̅̅̅ bisects ∠𝐶𝐴𝑁; 𝑚∠𝐶𝐴𝑅 = 43°
1. 𝑅𝐴
M
B
A
D
O
T
D
Reasons
P
O G
C
A
31. Given: 𝑚∠𝑀𝑂𝐷 = (2𝑥 − 2)°;
𝑚∠𝐵𝑂𝐷 = (9𝑥 + 17)°
Prove: 𝑥 = 15
D
M
O
B
32. Given: 𝑚∠𝐻𝑂𝑇 = (6𝑥 − 4)°;
𝑚∠𝑅𝑂𝐷 = (5𝑥 + 4)°
Prove: 𝑚∠𝑅𝑂𝐷 = 44°
R
H
O
D
T
33. Describe the transformation.
34. Graph the image after a reflection in the the line 𝑦 =
−1