ANSWER KEY
Name _______________________________________________
Date _____________________ Block __________
Use the figure below to answer questions 1 – 6. Assume that lines that appear to be parallel or
perpendicular are parallel and perpendicular, respectively.
parallel
1. ̅̅̅̅
𝐶𝐷 and ̅̅̅̅
𝐺𝐻 are __________________________
lines.
skew
2. ̅̅̅̅
𝐷𝐻 and ̅̅̅̅
𝐸𝐹 are __________________________
lines.
perpendicular
3. ̅̅̅̅
𝐴𝐶 and ̅̅̅̅
𝐴𝐸 are __________________________
lines.
4. Which line(s) are parallel to ̅̅̅̅
𝐸𝐺 ?
̅̅̅̅
𝐴𝐶 , ̅̅̅̅
𝐷𝐵, ̅̅̅̅
𝐻𝐹
5. Which line(s) are skew to ̅̅̅̅
𝐴𝐸 ?
̅̅̅̅
𝐶𝐷 , ̅̅̅̅
𝐷𝐵, ̅̅̅̅
𝐻𝐹 , ̅̅̅̅
𝐺𝐻
6. Which lines are perpendicular to ̅̅̅̅
𝐴𝐸 ?
̅̅̅̅
𝐶𝐴, ̅̅̅̅
𝐴𝐵, ̅̅̅̅
𝐺𝐸 , ̅̅̅̅
𝐸𝐹
7. Identify the following pairs of angles as vertical, corresponding, alternate interior, alternate
exterior, consecutive interior, linear pair, or none.
a. ∠1 and ∠11
Alternate Exterior Angles
Vertical Angles
c. ∠6 and ∠9
Alternate Interior Angles
d. ∠3 and ∠8
Corresponding Angles
2
1
b. ∠7 and ∠13
3
4
7
14
5
8
13
6
9
10
12
11
e. ∠7 and ∠3
No relationship
f. ∠12 and ∠11
Linear Pair
g. ∠6 and ∠10
Consecutive Interior Angles
h. ∠1 and ∠12
Since there is no such thing as consecutive exterior angles, these angles do not have a direct
relationship. However, there is an indirect relationship because it corresponds with ∠9 and ∠9 and ∠12
form a linear pair.
8. Using the figure in #7, are angles 3 and 8 congruent? How do you know?
We cannot determine that ∠3 ≌ ∠8 because the lines cut by the transversal
are not parallel.
Find the missing variables in each figure.
9. Angles are not drawn to scale.
(system of equations)
10.
(4y – 20)˚
44˚
y˚
7x˚
x=7
(3 + x)˚
28˚
x=4
y = 43
y = 10
(2x + 3y)˚
11.
12.
x=6
n = 13
y = 22
a = 74
Tell whether the lines through the given points are parallel, perpendicular, or neither.
13. Line 1: (3, -1) and (-2, 5)
Line 2: (-7, 2) and (-1, 7)
Parallel
15. Write an equation of the line that passes
through the point (5, -13) and is parallel
to the line y = 4x +2.
𝑦 = 4𝑥 − 33
14.
Line 1: (12, 7) and (10, 6)
Line 2: (4, 6) and (10,9)
Perpendicular
16. Use the same information from #12 to write
the equation of the perpendicular line.
1
47
𝑦=− 𝑥−
4
4
Graph the equations.
17.
2
3
18.
𝑦 =− 𝑥−4
−2𝑥 + 3𝑦 = −6
19. Line a is parallel to line b. Find the measures of ∠3, ∠4, and ∠5.
𝑚∠3 = 72˚
𝑚∠4 = 58˚
𝑚∠5 = 50˚
DO NOT ASSUME THE LINES ARE PARALLEL.
Circle whether the lines are parallel. Write the reason that supports your answer. Show all work.
20.
110
(3x + 7) (5x + 5)
21.
(6x – 21)
m
Not Parallel
(4x – 9)
45
x = 21
Circle: Parallel
22.
y 135
x
k
Is m  k ?
Circle: Parallel
Not Parallel
25
x=6
Circle: Parallel
Not Parallel
Why? Use the linear pair to solve for
x. Plug the value of x into 5x + 5. You
see that you get 110 so corresponding
angles are congruent.
Corresponding Angles Converse
Why? 45˚ corresponds with the
angle I have labeled as x and angle x
corresponds with the angle I have
labeled as y. Y forms a linear pair with
135˚ and 45 + 135 = 180.
23. Find the distance between the point and the line on the graph.
Refer to the last page of your notes
𝐷 = 2√13
Why? Use vertical angles to
solve for x. Plug x into the
unknown angles. The value of the
angles should be 25˚ because one
pair is alternate interior and the
other is corresponding. In both
cases, you get 15˚ therefore the
lines are not parallel.
24. Given: ∠1 ≌ ∠5
∠15 ≌ ∠5
l∥m
Prove:
Statements
Reasons
1. ∠15 ≌ ∠5
1. Given
2. ∠13 ≌ ∠15
2. Vertical Angles Congruence Theorem
3. ∠5 ≌ ∠13
3. Transitive Property of Congruence
𝑟∥𝑠
4.
4. Corresponding Angles CONVERSE
5. ∠1 ≌ ∠5
5. Given
l∥m
6.
6. Corresponding Angles CONVERSE
⃡ ⟘𝑈𝑆
⃡ ; 𝑇𝑄
⃡ ⟘𝑃𝑅
⃡
25. Given: 𝑇𝑄
𝑚∠2 = 𝑚∠3
Prove: ∠1 ≌ ∠4
Statements
Reasons
1.
⃡𝑇𝑄 ⟘𝑈𝑆
⃡ ; ⃡𝑇𝑄 ⟘𝑃𝑅
⃡
1. Given
2.
⃡ ∥ 𝑃𝑅
⃡
𝑈𝑆
2. Perpendicular Transversal Theorem
3.
3. Definition of Perpendicular Lines
4.
𝑚∠1 + 𝑚∠2 = 90˚
𝑚∠5 = 90˚
𝑚∠1 + 𝑚∠2 = 𝑚∠5
5.
𝑚∠5 = 𝑚∠3 + 𝑚∠4
5. Alternate Interior Angles Theorem
6.
𝑚∠1 + 𝑚∠2 = 𝑚∠3 + 𝑚∠4
6. Transitive Property of Equality
7.
𝑚∠2 = 𝑚∠3
7. Given
8.
𝑚∠1 + 𝑚∠2 = 𝑚∠2 + 𝑚∠4
8. Substitution
9.
𝑚∠1 = 𝑚∠4
9. Subtraction Property of Equality
10.
∠1 ≌ ∠4
10. Definition of Congruent Angles
4. Transitive Property of Equality