Name _______________________________________ Date ___________________ Class __________________
Parallel and Perpendicular Lines
Chapter Test
Circle the best answer.
Use the figure for Exercises 6 and 7.
1. Classify HG and AD.
A skew segments
B parallel segments
C perpendicular segments
D intersecting segments
2. If lines and m are skew, how many
planes contain two points of both lines?
F 0
H 2
G 1
J 3
3. Which are NOT alternate interior angles?
6. Given r || s  p, which angle is NOT
congruent to 4?
F 2
H 5
G 3
J 6
7. Given r  s  p, what is the measure of
1?
A 40°
C 110°
B 90°
D 140°
8. Which CANNOT be used to prove that
lines m and n are parallel?
A 3 and 6
C 2 and 3
F 2  4
B 2 and 7
D 4 and 5
G 4 is supplementary to 7.
4. The angles formed by two lines and a
transversal are labeled 1 through 8. If 1
and 8 are alternate interior angles and
1 and 5 are vertical angles, what type
of angle pair is 5 and 8?
F alternate exterior angles
G corresponding angles
H 4 is supplementary to 5.
J 1  5
9. Lines r and s are cut by a transversal
so that 1 and 2 are same-side
interior angles. If m1  (8x  40)°
and m2  (12x  20)°, for what value of
x is it true that r  s?
H alternate interior angles
A 6
C 30
J same-side interior angles
B 10
D 60
5. Which correctly completes the sentence?
When two lines are parallel, the acute
angles they form with a transversal are
________ to the obtuse angles.
A supplementary
B complementary
C congruent
D vertical
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Parallel and Perpendicular Lines
Chapter Test continued
10. If a transversal is perpendicular to one of
two parallel lines, which statement is
NOT correct?
13. Which is the justification for Step 5?
A 2 lines  to same line  2 lines 
F All the angles formed are congruent.
B 2 intersecting lines form linear pair of
 /s  lines 
G Every pair of angles is supplementary.
C  Transv. Thm.
H The transversal is  to the other line.
J Every pair of angles is complementary.
11. Which is a possible value of x?
A 21
C 25
B 23
D 26
Use the figure and the partially
completed proof for Exercises 12 and 13.
Given: AC is the shortest segment from A to
CD and m1  m2.
Prove: AB  AC
Proof:
Statements
Reasons
1. m1  m2
1. Given
2. ___?___
2. Given
3. AC  CD
3. Distance from a
point to a line
4.
4. Conv. of Alternate
Int. /s Thm.
?
5. AB  AC
5.
?
12. Which is the statement for Step 2?
F AB || CD
H AC  CD
G BD  CD
J Not here
D Same-Side Interior Angles Theorem
14. Given the point J(2, 4), for which point
K is JK a line with undefined slope?
F K(2, 4)
H K(4, 2)
G K(2, 4)
J K(2, 4)
15. If EF  GH for the points E(2, 5),
F(x, y), G(2, 2), and H(0, 0), which
is a possible ordered pair for F?
A (2, 1)
C (3, 1)
B (1, 4)
D (3, 10)
16. Given points A(1, 4), B(0, 4), C(2, 0),
and D(2, 5), what type of lines are AB
and CD ?
F parallel
H horizontal
G perpendicular
J vertical
17. Which is an equation of a horizontal line?
A x3
C yx
B y  4
D y  x
18. Which is the equation of a line that does
NOT go through the origin?
F x0
H yx
G yx1
J y  2x
19. Which line is NOT parallel to y 
A 2x  3y  6
2
x 2?
3
C 6y  12  4x
1
1
D 4x  6y  12
y  x 1
2
3
20. Which of the following is the equation of
the line that passes through (2, 1) and is
perpendicular to 5x  y  9?
B
F x  5y  3
G y  5x 
H x  5y  3
3
5
J y  5x 
3
5
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Holt McDougal Geometry
Name _______________________________________ Date ___________________ Class __________________
Parallel and Perpendicular Lines
Chapter Test continued
1. Identify a pair of skew segments.
7. Find the measure of QRS and state the
postulate or theorem that justifies your
answer.
________________________________________
2. Write True or False. Perpendicular lines
cannot be skew lines.
________________________________________
3. How many total pairs of both alternate
exterior and alternate interior angles are
formed by a transversal that intersects two
coplanar lines at two different points?
________________________________________
________________________________________
8. If 1  6 and m1  90°, is r  s?
________________________________________
4. Given: 8 and 6 are corresponding
angles. Identify the transversal.
________________________________________
9. Which values for x and y make lines
r, s, and t parallel?
________________________________________
5. If parallel lines are intersected by a
transversal that is not perpendicular to
them, how many pairs of nonadjacent
supplementary angles are formed?
________________________________________
6. What one word completes the following
sentence? ________ angles formed by a
transversal of parallel lines are congruent
and all the ________ angles are
supplementary to all the obtuse angles.
________________________________________
10. If two parallel lines and a transversal form
angles that are all congruent, describe
the relationship between the transversal
and each of the parallel lines.
________________________________________
________________________________________
________________________________________
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Holt McDougal Geometry
Name _______________________________________ Date ___________________ Class __________________
Parallel and Perpendicular Lines
Chapter Test continued
11. Write and solve an inequality for x.
15. If line r through (4, 4) and (6, 2) is
perpendicular to line s through (x, 1) and
(4, y), what are possible values
for x and y?
________________________________________
________________________________________
Use the partially completed two-column
proof for Exercises 12 and 13.
16. If line r through (1, 1) and (5, 7) is parallel
to line s through (4, 2) and
(x, y), what are possible values for
x and y?
________________________________________
Given: AD  BE and BCF  FCD.
17. Write True or False. All horizontal lines are
perpendicular to all vertical lines, so the
product of the slope of a horizontal line
and the slope of a vertical line is 1.
________________________________________
Prove: BE || CF
Proof:
Statements
Reasons
1. AD  BE
1. Given
2. BCF  FCD
2. Given
3. CF  AD
3.
?
4. BE || CF
4.
?
12. State the justification for Step 3.
________________________________________
________________________________________
18. Write True or False. Multiplying both sides
of the equation for a line by the same
nonzero number will produce an equation
for a line that coincides with the original
line.
________________________________________
19. Write the equation of the line that has
y-intercept 4 and is parallel to y  2.
________________________________________
20. Write an equation in slope-intercept form
for the line that passes through (6, 6) and
is perpendicular to 2x  3y  6.
________________________________________
13. State the justification for Step 4.
________________________________________
________________________________________
14. If the slope of a line is 0, which type
of line is it and what is true about the
y-coordinates of all points on the line?
________________________________________
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Holt McDougal Geometry
Name _______________________________________ Date ___________________ Class __________________
Answer Key Parallel and
Perpendicular Lines
20. y  
3
x  15
2
Chapter Test Multiple Choice
1. A
11. A
2. F
12. J
3. C
13. C
4. G
14. J
5. A
15. D
6. G
16. G
7. C
17. B
8. H
18. G
9. A
19. D
10. J
20. H
Chapter Test Free Response
1. Sample answer: AB and EH
2. True
3. four
4. line s
5. eight
6. acute
7. 72; Same-Side Interior Angles Theorem
8. no
9. x  26.25 and y  3.75
10. The transversal is perpendicular to both
parallel lines.
11. 4x  3  2x  11; x  7
12. 2 intersecting lines form linear pair of
 s  lines 
13. 2 lines  to same line  2 lines
14. horizontal line; all the same
15. Sample answer: x  3, y  0
16. Sample answer: x  6, y  1
17. False
18. True
19. y  4
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry