1.
Which diagram suggests a correct construction of a line parallel to given line l and passing through
given point Q? (1 point)

(0 pts)

(1 pt)

(0 pts)

(0 pts)
1 /1 point
2.
Find the values of x and y. The diagram is not to scale.
(1 point)

(0 pts) x = 68, y = 75

(1 pt) x = 75, y = 68

(0 pts) x = 40, y = 68

(0 pts) x = 75, y = 70
1 /1 point
3.
What is the relationship between
2 and
7?
(1 point)

(0 pts) corresponding angles

(0 pts) same-side interior angles

(1 pt) alternate exterior angles

(0 pts) alternate interior angles
1 /1 point
4.
Construct the line perpendicular to
(1 point)
at point V.

(0 pts)

(1 pt)

(0 pts)

(0 pts)
0 /1 point
5.
Find the value of x so that f
g. The diagram is not to scale.
(1 point)

(0 pts) 19

(1 pt) 18

(0 pts) 17

(0 pts) –18
1 /1 point
6.
Which two lines are parallel?
I. 4y = 3x + 1
II. 4y = 3x – 1
III. 3y = 4x – 1 (1 point)

(0 pts) II and III

(0 pts) I and III

(1 pt) I and II

(0 pts) none of the above
1 /1 point
7.
The folding chair has different settings that change the angles formed by its parts. Suppose m
2 is 31 and m
(1 point)

(0 pts) 123
3 is 72. Find m
1. The diagram is not to scale.

(0 pts) 113

(0 pts) 93

(1 pt) 103
0 /1 point
See #10 in guided notes from review for a similar problem. We said that you can add
the two remote interior angles to find the measure of the exterior angle. So 31 + 72 = 103 degrees
for <1.
8.
Is the line through points P(–7, 2) and Q(7, –6) parallel to the line through points R(–1, –5) and S(–3,
–1)? Explain. (1 point)

(0 pts) No; one line has zero slope, the other has no slope.

(0 pts) Yes; the lines are both vertical.

(0 pts) Yes; the lines have equal slopes.

(1 pt) No; the lines have unequal slopes.
1 /1 point
9.
Construct the line that is perpendicular to the given line through the given point.
(1 point)

(1 pt)

(0 pts)

(0 pts)

(0 pts)
0 /1 point
10.
Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y = –9x – 9.
A perpendicular brace passes through the point (–1, 7). Write an equation of the line that contains the
brace. (1 point)

(0 pts) y – 1 = –

(0 pts) x – 7 = –9(y + 1)

(1 pt) y – 7 =

(0 pts) y – 7 = –9(x + 1)
(x + 7)
(x + 1)
0 /1 point
See #23 in guided notes from review for a problem just like this. You need to find a
slope that would be perpendicular to -9, so flip it and change sign to get 1/9. Then plug in that slope
and the point (-1, 7) into the point slope form (y – y1) = m(x – x1) ( y – 7) = 1/9(x - -1) (y – 7) =
1/9(x + 1) The one you chose has the same slope of -9 as the original line, so it would be parallel, not
perpendicular.
11.
What is the graph of –3x – 8y = 24? (1 point)

(1 pt)

(0 pts)

(0 pts)

(0 pts)
0 /1 point
See #5 in the Unit 3 Lesson 7 notes for the exact same problem, or look at review
notes #13 for a similar problem. Need to find x and y intercepts. -3x = 24 so x = -8 -8y = 24 so y = 3 Need to find the graph that crosses x axis at -8 and crosses the y axis at -3.
12.
Identify a pair of alternate interior angles.
(1 point)

(0 pts)
2 and
6

(0 pts)
1 and
2

(0 pts)
4 and
7

(1 pt)
3 and
7
1 /1 point
Short Answer
Your teacher will grade your responses to questions 13–22 to ensure that you receive proper credit for
your answers.
13.
Write an equation in point-slope form of the line through point J(4, 1) with slope –4. (1 point)
Essay:
y-1= -4(x-4).
1 /1 point
14.
Write the equation for the horizontal line that contains point G(–8, 8). (1 point)
Essay:
y=8.
1 /1 point
15.
Which lines are parallel if m
4=m
5? Justify your answer.
(1 point)
Essay:
Lines R and S are parallel by the converse of alternate exterior angles.
0 /1 point
<4 and <5 are alternate interior angles
16.
Complete the two-column proof.
Given: ∠2 and ∠5 are supplementary
Prove:
Statements
Reasons
1. _____________
2. ∠ 3
1. _____________
2. _____________
∠2
3. ∠ 3 and ∠ 5 are supplementary 3. _____________
4. _____________
4. _____________
(6 points)
Essay:
Angles 2 and 5 are supplemenary; given.
Vertical angles.
Substitution.
l || m; Converse of Same Side Interior Angles Thereom.
6 /6 points
17.
The map given shows the relationship among three streets. Suppose that m
Are Maple Street and Elm Street parallel? Explain.
1+m
2 = 180°.
(4 points)
Essay:
Maple Street and Elm Street are both parallel, because they do not intersect one another. Even though
River Drive goes through both of the two Streets, Maple Street and Elm Street don't touch.
2 /4 points
Need to justify with one of the converses we learned to prove lines parallel. In this
case it is Converse of Same Side Interior Angles.
18.
Write a paragraph proof of this theorem: In a plane, if two lines are perpendicular to the same line,
then they are parallel to each other.
Given: r
s, t
s
Prove: r || t
(4 points)
Essay:
Angles 2 and 6 are right angles by the definition of perpendicular. So angle 2 = ~ angle 6. Since
corresponding angles are congruent, r||t.
4 /4 points
19.
Note: Remember to show all of the steps that you use to solve the problem. You can use the
comments field to explain your work. Your teacher will review each step of your responses.
What is the slope of the line shown?
(2 points)
2 /2 points
Okay, but -4-5 = -9 so it should be -9/11 Also, the line falls from left to right, so it is
negative slope.
20.
What is an equation for the line that passes through points (–1, –4) and (1, 4)? Write the equation in
slope-intercept form. (2 points)
1 /2 points
slope is 4, but if you graph it like we did in the live lesson, you should see that the yintercept is zero. y = 4x + 0
21.
Find the values of x, y, and z. The diagram is not to scale.
(3 points)
3 /3 points
Okay, explanation is correct, but you have the letters swtiched in your final answer. x
= 81, y = 68, z = 99
22.
Write the equation for the vertical line that contains point E(10, –3). (2 points)
2 /2 points
Essay
Note: Your teacher will grade your responses to questions 23–24 to ensure you receive proper credit
for your answers.
23.
Given
, explain how to construct a square with sides of length AB. (4 points)
Essay:
Draw a line with the length of AB and label it CD. Draw a perpendicular line to the side that you drew
and then draw parallel lines to AB from C and D. Then Draw another line and label EF and connect EF.
1 /4 points
See Unit 3 Lesson 6 guided notes where we did this problem together in the lesson.
24.
Is the line through points P(–8, –10) and Q(–5, –12) perpendicular to the line through points R(9, –6)
and S(17, –5)? Explain.
(2 points)
Essay:
No, because (-2/3) times (1/8) -1.
1 /2 points
When you multiply them, they do NOT equal -1. Slopes are not negative reciprocals.