Geometry Chapter 3 Review
Short Answer
1. 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.
2. Find
The diagram is not to scale.
Q
b
1 2
3 4
a
5 6
7 8
c
R
68°
42°
3. Find the value of the variable if
and
not to scale.
1
2
3
This diagram of airport runway intersections
shows two parallel runways. A taxiway crosses
both runways.
The diagram is
l
4
5
6
7
m
8
4. Find the values of x and y. The diagram is not to
scale.
6. If 8 measures 105, what is the sum of the
measures of 1 and 4?
7. Line r is parallel to line t. Find m 5. The diagram
is not to scale.
(x – 5)°
52°
(y + 5)°
69°
5. If
and
, what is
r
7
142°
1
l
38°
76°
3
x°
m
t
4
2
5
6
9.
. Find the value of x for p
to be parallel to q. The diagram is not to scale.
8. Find the value of x for which l is parallel to m. The
diagram is not to scale.
3 4
5
p
1 2
6
q
Other
10. Given
, what can you conclude about the lines l, m, and n? Explain.
n
1
l
2
l
m
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
11. Which statement is true?
a.
are alternate interior
angles.
c.
are same-side angles.
b.
are alternate interior
d.
are same-side angles.
angles.
12. Is the line through points P(5, –8) and Q(10, –10) perpendicular to the line through points R(–2, 8) and S(–4, 13)?
Explain.
a. No, their slopes are not reciprocals.
c. Yes; their slopes are equal.
b. Yes; their slopes have product –1
d. No, their slopes are not opposite
reciprocals.
y
13. Which lines, if any, can you conclude are parallel
b.
given that
? Justify your
6
conclusion with a theorem or postulate.
4
2
g
1
–6
2
j
–4
–2
2
4
6
x
2
4
6
x
–2
h
–4
k
–6
a.
, by the Converse of the Consecutive
Interior Angles Theorem
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 Consecutive
Interior Angles Theorem
6
4
2
–4
–2
–2
y
–4
6
–6
4
2
–4
y
–6
14. Graph y = 3 x – 3.
a.
–6
c.
–2
2
–2
–4
–6
4
6
x
d.
b.
y
y
8
6
6
4
4
2
–6
–4
2
–2
2
4
6
–8 –6 –4 –2
–2
x
–2
2
4
6
8
x
2
4
6
8
x
2
4
6
8
x
–4
–4
–6
–6
–8
c.
y
8
15. Write an equation in slope-intercept form of the
line through points S(3, –7) and T(4, 2).
a. y = 9 x – 34
9 x + 34
b.
c. y = 9 x + 34
9 x – 34
d.
16. Graph
a.
6
4
2
–8 –6 –4 –2
–2
–4
.
–6
y
8
–8
6
d.
4
y
8
2
6
–8 –6 –4 –2
–2
2
4
6
8
x
4
–4
2
–6
–8 –6 –4 –2
–2
–8
–4
–6
–8
This diagram of airport runway intersections
shows two parallel runways. A taxiway crosses
both runways.
d. none of these
18. Which angles are corresponding angles?
a.
b.
c.
d. none of these
17. How are 6 and 4 related?
a. corresponding angles
b. alternate interior angles
c. consecutive interior angles
19. Is the line through points P(7, 0) and Q(–2, 4) parallel to the line through points R(–5, 2) and S(4, 0)? Explain.
a. Yes; the lines are both vertical.
c. No, the lines have unequal slopes.
b. No, one line has slope, the other has no
d. Yes; the lines have equal slopes.
slope.
20. Which two lines are parallel?
I.
II.
III.
a. I and II
c. II and III
b. I and III
d. No two of the lines are parallel.
21. Write an equation for the line parallel to y = –5x –
23. At the curb a ramp is 10 inches off the ground. The
11 that contains P(7, –7).
other end of the ramp rests on the street 70 inches
a. y = -7x + 57
straight out from the curb. Write a linear equation
b. y = -7x + 69
in slope-intercept form that relates the height y of
c. y = 7x - 69
the ramp to the distance x from the curb.
d. x = 7y - 69
a. y = 7 x + 10
b.
1
y =  x + 70
7
22. Write an equation in slope-intercept form of the
c.
1
y =  x + 10
line through point P(2, –7) with slope 3.
7
a. y = 3x – 13
d.
1
b. y = -5x + 5
y = x + 70
7
c. y = -5x - 49
d. y = 3x – 7
24. Plans for a bridge are drawn on a coordinate grid.
One girder of the bridge lies on the line y = 4x – 6.
A perpendicular brace passes through the point (–3,
–5). Write an equation of the line that contains the
brace.
a. x = 2y + 24
Numeric Response
b. y = 2x + 24
c.
y=- x+
d. x = 3y + 28
25. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given:
Prove:
Geometry Chapter 3 Review
Answer Section
SHORT ANSWER
1.
2.
3.
4.
5.
6.
7.
8.
9.
The rowers keep corresponding angles congruent.
70
7
x = 74, y = 54
90
210
142
38
55
OTHER
10. l and m are both perpendicular to n. Explanation: Since l and m are parallel,
are supplementary by the
Same-Side Interior Angles Theorem. It is given that
, so 180 = m1 + m2 = m1 + m1 = 2m1,
and m1 = 90 = m2. Since 1 and 2 are right angles, l is perpendicular to n and m is perpendicular to n.
MULTIPLE CHOICE
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
A
D
A
A
A
A
C
A
C
A
A
A
C
C
NUMERIC RESPONSE
25. a. Corresponding angles.
b. Vertical angles.
c. Transitive Property.