2.5 Prove Lines Parallel
Name __________________________________ Per ________
5. Is it possible to prove that lines p and q are parallel? If so, state the converse you would use.
a)
b)
c)
p
140°
d)
q
140°
6. If 𝑘 ∥ 𝑗 where 𝑚∠7 = (9𝑥 − 1)°and 𝑚∠1 = (14 + 4𝑥)° then
find the measure of ∠1. EXPLAIN!
7. Which of the following statement must be true
given ∠4 and ∠7 are supplementary? CHOOSE
ALL THAT APPLY.
2 3
1 4
A. ∠3 ≅ ∠2
k
5 7
6 8
2 3
1 4
B. 𝑚∠2 + 𝑚∠7 = 180
5 7
6 8
C. ∠1 ≅ ∠5
j
D. ∠2 ≅ ∠8
P
M
8. Given : ∠1 ≅ ∠2
Prove: 𝑎 ∥ 𝑏
9. Given
: 𝑎∥𝑏
O
Prove: ∠1 ≅ ∠2
1
a
b
2
Q
P
H
A
T U
a
1
L
b
2
G
Q
10. Given: ∠1 ≅ ∠3; 𝑚∠4 = 55°
Prove: 𝑚∠8 = 55°
m
1
8
n
2
3
7
6
5
j
n
1
2
4
3
5
Reasons
1.
2. 𝑚 ___ 𝑛
2. corr ∠s ≅ ⇒ ∥ lines
3.
3. ∥ lines ⇒ _____________________
4.
4.
4
11. Given: 𝑚∠6 = 𝑚∠7
𝑚∠1 = 56°
Prove: 𝑚∠3 = 56°
k
Statements
1.
6
7
m
12. Given: ∠5 ≅ ∠6;
𝑚∠1 = (2𝑥 + 5)°;
𝑚∠2 = (3𝑥 − 13)°
Prove: 𝑥 = 18
g
m
1
5
n
2
6
13. Given: ∠2 ≅ ∠3
𝑚∠5 = (30𝑥 + 25)°,
𝑚∠4 = (8𝑥 + 3)°
Prove: 𝑚∠4 = 35°
r
w
4
s
3
5
2
k
14. Given: 𝑎 ∥ 𝑏; 𝑚∠4 = (12𝑥 + 1)°
𝑚∠5 = (15𝑥 + 17)°
Prove: 𝑚∠4 = 73°
a
2 1 4
3
b
6
5
7
8
15. Given: 𝑚∠𝐻𝐾𝐽 = (6𝑥 − 4)°
𝑚∠𝐽𝐾𝐺 = (10𝑥 − 8)°
Prove: 𝑥 = 12
I
H
G
K
J
17. Solve for 𝑥. Explain.
16. Which of the following correctly describes the
transformation shown below?
A. Rotation 180°
B. Reflection in the 𝑥
axis
C. Reflection in the 𝑦
axis
D. Rotation 90°
clockwise
18. Using a STRAIGHTEDGE and a COMPASS only, copy
the angle shown below.
a
19. Using a STRAIGHTEDGE and a COMPASS
only,
1
construct a line parallel to the2 line
shown
below
that
3 4
b
passes through 𝑄.
5
6
7 8
Q
I
L
20. Solve for 𝑥. Explain.
a
214
3
6 58
7
H
O
b
K
21.GDescribe the transformation
J
A
B C'
C B'
22. Solve for 𝑥. Explain.
A'
23. Using a STRAIGHTEDGE and a COMPASS only,
constuct a line through point 𝐺 that is perpendicular to
the given line.
F
E
G