A.
B.
C.
GEOM CH. 3.1.-3.5 REVIEW
are alternate angles.
are alternate angles.
are same-side interior
angles.
K
L
D.
M
J
____
are same-side interior
angles.
5. Which is a correct two-column proof?
Q
P
N
____
Given:
Prove:
R
and
a
1. What four segments are parallel to plane MRQL?
A. segments JK, KL, C. segments JK, JN,
JM, and ML
NP, and KP
B. segments NP, KP, D. segments JM, KL,
PQ, and JN
NR, and PQ
are supplementary.
b
c
r
d
e
f
g
h
s
Use the diagram to find the following.
A.
h
a
1
2
8
b
3
7
4
6
5
B.
____
____
2. Identify a pair of alternate exterior angles.
A.
C.
B.
D.
3. Which angles are corresponding angles?
C.
____
A.
C.
B.
D. none of these
4. Which statement is true?
____
D. none of these
6. Find
The diagram is not to scale.
Q
R
77°
47°
____
A. 66
7. Find
B. 56
C. 124
D. 103
The diagram is not to scale.
3 4
5
6
g
>>
>
>
P
1 2
>>
j
____
106°
k
A. 106
B. 74
8. Find the value of x.
to scale.
C. 64
D. 84
. The diagram is not
80°
l
64°
q
A. 108
B. 13
C. 117
D. 126
____ 11. Find the value of x for which l is parallel to m.
The diagram is not to scale.
( 3 x - 43 )º
2x
____
p
h
l
m
A. 100
B. 80
C. 123
D. 41
____ 12. Each sheet of metal on a roof is perpendicular to
the top line of the roof. What can you conclude
about the relationship between the sheets of
roofing? Justify your answer.
m
A. 148
B. 116
C. 64
9. Which lines are parallel if
Justify your answer.
D. 32
?
g
1
j
A.
2
h
k
, by the Converse of the Same-Side
Interior Angles Postulate
B.
, by the Converse of the Alternate
Interior Angles Theorem
C.
, by the Converse of the Alternate
Interior Angles Theorem
D.
, by the Converse of the Same-Side
Interior Angles Postulate
____ 10. Find the value of x for which p is parallel to q, if
.The diagram is not ____
to scale.
A. The sheets of metal are all parallel to each
other by the Transitive Property of Parallel
Lines.
B. The sheets of metal are all parallel to each
other by the Alternate Interior Angles
Theorem.
C. The sheets of metal are all parallel to each
other because in a plane, if a line is
perpendicular to one of two parallel lines,
then it is also perpendicular to the other.
D. The sheets of metal are all parallel to each
other because in a plane, if two lines are
perpendicular to the same line, then they are
parallel to each other.
13.Find the value of k. The diagram is not to scale.
y
75°
8
6
(1, 6)
4
2
k°
33°
–8 –6 –4 –2
–2
(–6, –3)
–4
A. 72
B. 108
C. 105
D. 42
____ 14. Find the value of x. The diagram is not to scale.
2
4
6
8
x
–6
–8
72°
A.
C. 7
9
B. 9
D. 9

7
7
105°
x°
3
____ 20. What is the graph of y =  x – 2?
4
A. 33
B. 162
C. 147
D. 75
A
C
____ 15. Find the value of x. The diagram is not to scale.
.
.

7
9
110°
y
6
y
57°
x°
A. 33
B. 70
C. 23
D. 13
____ 16. The folding chair has different settings that
change the angles formed by its parts. Suppose
is 34 and
is 76. Find
. The
diagram is not to scale.
6
4
4
2
2
–6
–4
–6
–2
2
4
6
–4
–2
4
6
x
–4
–4
–6
–6
B
.
1
2
–2
x
–2
D
.
2
3
y
y
6
6
A. 130
B. 110
C. 100
D. 120
____ 17.
NO QUESTION
____ 18.
NO QUESTION
____ 19. What is the slope of the line shown?
4
4
2
2
–6
____
–4
–2
2
4
6
x
–6
–4
–2
2
–2
–2
–4
–4
–6
–6
4
6
x
21.What is the graph of
A
.
?
C
.
y
–6
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–2
–6
–4
–2
2
4
2
4
–2
–4
–4
–6
–6
B
.
D
.
y
–6
–4
y
6
6
4
4
2
2
–2
2
–2
4
6
x
–6
–4
–2
____ 26. Is the line through points P(–3, –2) and Q(2, 3)
perpendicular to the line through points R(10, –
1) and S(15, –6)? Explain.
A. No, their slopes are not opposite reciprocals.
B. No; their slopes are not equal.
C. Yes; their slopes have product –1.
D. Yes; their slopes are equal.
____ 27. What is an equation in point-slope form for the
line perpendicular to y = 2x + 13 that contains
(8, –4)?
A.
C. y + 4 = 2(x – 8)
1
y + 4 =  (x – 8)
2
6
x
B. x + 4 = 2(y – 8)
D.
1
y + 8 =  (x – 4)
2
____ 28. Give the slope-intercept form of the equation of
the line that is perpendicular to
–7x – 8y = 12 and contains P(–3, 1).
A.
C.
8
8
31
y – 3 = (x + 1)
y= x+
7
7
7
B.
D.
8
29
8
y= x
y – 1 = (x + 3)
7
7
7
29. Give the missing reasons in this proof of the
Alternate Interior Angles Theorem.
6
–2
–4
–4
–6
–6
____ 22. Write an equation in point-slope form of the line
through point J(4, –4) with slope 4.
A.
C.
B.
D.
____ 23. What is an equation for the line that passes
through points (4, –4) and (8, 4)?
A. (y – 4) = 2(x + 4)
C. (y – 4) = –2(x + 4)
B. (y + 4) = 2(x – 4)
D. (y + 4) = –2(x – 4)
____ 24. Is the line through points P(3, –5) and Q(1, 4)
parallel to the line through points R(–1, 1) and
S(3, –3)? Explain.
A. Yes; the lines have equal slopes.
B. No; the lines have unequal slopes.
C. No; one line has zero slope, the other has no
slope.
D. Yes; the lines are both vertical.
____ 25. What is the equation in point-slope form for the
line parallel to y = 5x – 4 that contains P(–6, 1)?
A. x – 1 = –5(y + 6)
C. y – 1 = –5(x + 6)
B. y + 1 = 5(x + 6)
D. y – 1 = 5(x + 6)
x
Given:
Prove:
30. The 8 rowers in the racing boat stroke so that the
angles formed by their oars with the side of the
boat all stay equal. Explain why their oars on
either side of the boat remain parallel.
31. Find the measure of each interior and exterior
angle. The diagram is not to scale.
j
5
4
115 o
k
6
l
1
2
>
>
9
8
3
7
32. Identify the form of the equation –3x – y = –2.
To graph the equation, would you use the given
form or change to another form? Explain.
33. Write a two-column proof.
Given:
Prove:
are supplementary.
1
2
3
l
4
5
6
7
8
m
34. Find the values of the variables. Show your
work and explain your steps. The diagram is not
to scale.
o
31
x
w
v
y
o
68
z
35. In a plane, line k is parallel to line l and line j is
perpendicular to line l. What can you conclude
about the relationship between lines j and k?
36. Line p contains points A(–7, –9) and B(4, 0).
Line q is parallel to line p. Line r is
perpendicular to line q. What is the slope of line
r? Explain.
GEOM CH. 3.1.-3.5 REVIEW
Answer Section
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
A
C
C
A
B
B
D
A
B
D
D
A
A
D
B
A
C
B
B
C
B
B
B
D
C
A
C
29. ANS:
a. Corresponding angles
b. Vertical angles
c. Transitive Property
30. ANS:
The rowers keep corresponding angles congruent.
31. ANS:
32. ANS:
Standard form. Answer may vary. Sample: You could use the given form. Find the intercepts and use them to
draw the line.
33. ANS:
[4]
[3]
[2]
[1]
correct idea, some details inaccurate
correct idea, some statements missing
correct idea, several steps omitted
PTS: 1
34. ANS:
[4] Because the three interior angles of a triangle have measures with sum 180, w + 31 +
90 = 180, so w = 59. Because vertical angles are congruent, y = 59. Because
supplementary angles have measures with sum 180, x = v = 121.
Because the three interior angles of a triangle have measures with sum 180, z + 68 +
y = z + 68 + 59 = 180, so z = 53.
[3] small error leading to one incorrect answer
[2] three correct answers, work shown
[1] two correct answers, work shown
35. ANS:
Lines j and k are perpendicular. It is given that line k is parallel to line l and line j is perpendicular to line l
Therefore, line j is perpendicular to k, because in a plane, if a line is perpendicular to one of two parallel lines,
then it is also perpendicular to the other.
36. ANS:
11
 ; Line r is perpendicular to line p because a line perpendicular to one of two parallel lines is also
9
perpendicular to the other. Thus, the slope of line r is the opposite reciprocal of the slope of line p.