Download Spring Break Packet

2010 Geometry Spring Break Packet
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1. Based on the pattern, make a conjecture about the sum of the first 20 positive even
numbers.
2
=
2 =
2+4
=
6 =
2+4+6
= 12 =
2+4+6+8
= 20 =
2 + 4 + 6 + 8 + 10
= 30 =
a. The sum is
b. The sum is
____
.
.
c. The sum is
d. The sum is
.
2. According to the pattern, make a conjecture about the product of 13 and 8,888,888.
88 = 1144
888 = 11,544
8888 = 115,544
88,888 = 1,155,544
____
a. 115,555,544
c. 1,155,555,544
b. 1,115,555,444
d. 11,155,555,444
3. ____ two points are collinear.
a. Any
b. Sometimes
c. No
4. How many pairs of skew lines are shown?
____
a. 24
5. Find AC.
____
.
b. 12
A
c. 48
B
C
d. 4
D
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
a. 14
b. 15
c. 12
d. 4
____
6. A high school soccer team is going to Columbus to see a professional soccer game. A
coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3,
4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop
halfway between the cities. What are the coordinates of the rest stop? What is the
approximate distance between the high school and the stadium? (One unit 6.4 miles.)
c.
a.
, 5 miles
, 32 miles
b.
____
, 160 miles
d.
, 16 miles
7. Find the perimeter of the rectangle. The drawing is not to scale.
47 ft
57 ft
____
a. 151 feet
b. 208 feet
8. Find the area of the circle in terms of π.
c. 161 feet
d. 104 feet
30 in.
b. 900π in.2
c. 60π in.2
d. 225π in.2
a. 30π in.2
____ 9. If the perimeter of a square is 72 inches, what is its area?
b. 324
c. 18
d. 5,184
a. 72
____ 10. Which statement is the Law of Syllogism?
a. If
is a true statement and p is true, then q is true.
b. If
is a true statement and q is true, then p is true.
c. if
and
are true statements, then
is a true statement.
d. If
and
are true statements, then
is a true statement.
____ 11. What can you conclude from the information in the diagram?
P
U
S
Q
R
T
a. 1.
2.
3.
are vertical angles
b. 1.
2.
3.
are adjacent angles
c. 1.
2.
is a right angle
3.
are vertical angles
d. 1.
2.
is a right angle
3.
are adjacent angles
____ 12. Find the values of x and y. The diagram is not to scale.
(x – 3)°
41°
(y + 8)°
74°
a. x = 77, y = 59
b. x = 77, y = 57
c. x = 57, y = 77
d. x = 41, y = 57
____ 13. Which is a correct two-column proof?
Given:
and
are supplementary.
Prove:
C
P Q
R S
T U
V W
a.
b.
c.
d. none of these
B
Y
____ 14.
. Find the value of x for p to be parallel to q. The diagram is not to
scale.
3 4
5
1 2
6
p
q
a. 114
b. 126
c. 120
____ 15. Classify the triangle by its sides. The diagram is not to scale.
9
d. 20
9
9
a. straight
b. scalene
c. isosceles
d. equilateral
____ 16. The folding chair has different settings that change the angles formed by its parts. Suppose
is 26 and
is 70. Find
. The diagram is not to scale.
1
2
3
a. 96
b. 106
c. 116
d. 86
____ 17. The jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as
shown here. The box uses two pairs of congruent right triangles made of foam to fill its four
corners. Find the measure of the foam angle marked.
x
a. 18°
x
b. 54°
c. 36°
d. 72°
____ 18. Find
. The diagram is not to scale.
96°
118°
115°
104°
A
a. 107
b. 117
c. 63
d. 73
____ 19. Write an equation in point-slope form, y – y1 = m(x – x1), of the line through points (4, –4)
and (1, 2) Use (4, –4) as the point (x1, y1).
a. (y – 4) = –2(x + 4)
c. (y + 4) = 2(x – 4)
b. (y – 4) = 2(x + 4)
d. (y + 4) = –2(x – 4)
1
____ 20. Graph the line that goes through point (–5, 5) with slope .
5
y
y
a.
c.
–6
–4
6
6
4
4
2
2
–2
2
4
6
x
–2
–4
–4
–6
–6
d.
y
–4
–4
–2
b.
–6
–6
–2
6
4
4
2
2
2
4
6
x
4
6
x
2
4
6
x
y
6
–2
2
–6
–4
–2
–2
–2
–4
–4
–6
–6
____ 21. 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.
____ 22. Is the line through points P(0, –9) and Q(2, –8) perpendicular to the line through points R(1,
4) and S(3, 3)? Explain.
a. Yes; their slopes are equal.
b. Yes; their slopes have product –1
c. No, their slopes are not reciprocals.
d. Yes; their slopes have product –1
____ 23. Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y
= 3x – 3. A perpendicular brace passes through the point (–7, 9). Write an equation of the
line that contains the brace.
a.
c. x – 9 = 3(y + 7)
1
y – 7 = (x + 9)
3
b. y – 9 = 3(x + 7)
d.
1
y – 9 = − (x + 7)
3
____ 24. What must be true about the slopes of two perpendicular lines, neither of which is vertical?
a. The slopes are equal.
b. The slopes have product 1.
c. The slopes have product –1.
d. One of the slopes must be 0.
____ 25. Construct the line perpendicular to
Q
S
at point M.
R
a.
c.
K
M
L
b.
K
M
L
K
M
L
d.
K
M
L