Download Accelerated Geometry B/Algebra 2 Summer Work Name: Please

Accelerated Geometry B/Algebra 2 Summer Work
Name: _________________________________
Please complete each of the following questions. You may use a calculator but you should show all steps to problem
solving. You will turn this in to Ms. Shaffer on the first day of your class.
Please seek tutoring if topics covered in this packet are unfamiliar or you do not remember the concepts. It is
expected that ALL students entering Accelerated Geometry B/Algebra 2 have had exposure to this material. We will
not be covering this material in our class, but you will be tested on these concepts.
1. A company ships sand to customers for their aquariums. To ship the sand, they use tubes with a 4 cm radius and cut the
tubes to whatever height is needed. The sand they sell has a density of 1.41 grams per cubic centimeter. If Jerry buys
2,100 grams of sand, then approximately how high will the tube be that the sand is shipped in?
2. Some farms use a hay elevator to move bales of hay to the second story of a barn
loft. The bottom of the elevator is 9 meters from the barn and the elevator makes an
angle of 34° with the ground. What is the height of the barn from the bottom of the
barn opening to the ground?
3. Which of the following reasons completes the proof below?
A. SSA
B. SSS
C. AAS
D. ASA
Given: Kite PRST.
Prove: RQS
TQS
Proof:
Statements
Reasons
1. RS
RP
Definition of a kite
TS
TP
2. S is equidistant from R and T
Definition of congruent segments
P is equidistant from R and T
3. SP is the
bisector of RT
If a point is equidistant from the endpoints of a segment,
then it is on the perpendicular bisector of the segment.
4. Q is equidistant from R and T
If a point is on the perpendicular bisector of a segment,
then it is equidistant from the endpoints of the segment.
5. RQ
TQ
Definition of a segment bisector
6. SQ
SQ
Reflexive property of congruence
7. RQS
TQS
4. Ron is designing a new slide for the amusement park in town. The slide makes an
angle of 39 ° with the ground. The top of the slide is to be 9 feet off the ground. What
should be the length of the slide he needs to make to the nearest foot?
5. The circumference of the earth is approximately 24,901 miles. The circumference of the earth's moon is about 72.76%
smaller than the earth's circumference. What is the approximate radius of the earth's moon?
6. Figure JKLMN was changed to create figure PQRST. Determine if figure JKLMN is similar to figure PQRST.
A.
Figure JKLMN is similar to figure PQRST because dilation (x,y) to (3x,3y) maps figure JKLMN to figure PQRST.
Figure JKLMN is not similar to figure PQRST because geometric stretch (x,y) to (2x,3y) maps figure JKLMN to
B. figure PQRST.
Figure JKLMN is not similar to figure PQRST because geometric stretch (x,y) to (3x,2y) maps figure JKLMN to
C. figure PQRST.
D.
Figure JKLMN is similar to figure PQRST because dilation (x,y) to (2x,2y) maps figure JKLMN to figure PQRST.
7. If X = 27 inches, Y = 120 inches, and Z = 123 inches, what is the cosine of
8. The vertices of a triangle are listed below. What is the area of the triangle?
K(-2, 2), L(2, 2), M(0, -3)
B?
9. If
= 41° and m = 46 cm, what is the value of n to the nearest tenth of a centimeter?
10. Given that the diameter of Circle E is 14 cm, and the radius of Circle F is 10 cm, what can be concluded about the two
circles?
A. the circles are similar and congruent
B. the circles are neither similar nor congruent
C. the circles are congruent only
D. the circles are similar
11. Which of the following transformations preserves the lengths of the sides of the figure?
A. reflection
B. dilation
C. contraction
D. expansion
12. In the figure, the measure of m is 34° and the measure of
Determine how the triangles can be shown to be similar.
p is 146°.
A. The triangles are not similar to each other.
B. The triangles are similar by AA.
C. The triangles are similar by SSS.
D. The triangles are similar by SAS.
13. Yvonne is constructing a line perpendicular to
and passing through point A on
using only a compass and a
straightedge. She has drawn arcs with a compass of set width centered at point A intersecting
in two places. Yvonne
labeled the points of intersection B and C. Which of the following sentences describes her next step in the construction?
A. Place the compass needle on point B and set the width of the compass beyond point A.
B. Place the compass needle on point A and set the width to half way between points B and A.
C. Place the compass needle on point B and set the width to point A.
D. Place the compass needle on point A and set the width beyond point B.
14. Garry is playing with billiard balls. He wants to design a glass plane for playing so that he can roll the billiard balls
down the plane. The plane has a vertical height of 2 feet and a slant length of 10 feet. What is the angle the glass plane
will make with the ground?
15. In the figure below, STU is congruent to VWU. If m UWV = 42° and
m WUV = 113°, what is the measure of UST?
16. The vertices of a triangle are listed below.
Which of the following can be used to describe the triangle?
I. acute
II. obtuse
III. right
IV. scalene
V. isosceles
A. II and IV only
B. III and IV only
C. II and V only
D. I, II, and IV only
17. Which of the following statements and reasons completes the proof below?
A. m 1 = m 4 since vertical angles are congruent.
B. m
1+m
2=m
C. m
2=m
2 by the reflexive property.
D. m
1+m
2=m
Given:
1+m
2+m
5 by the transitive property of equality.
5 by the transitive property of equality.
1 and 2 are a linear pair
2 and 5 are supplementary
Prove: r
s
Proof:
Statements
Reasons
1.
1 and 2 are a linear pair
given
2 and 5 are supplementary
2.
1 and
3. m
m
2 are supplementary linear pair property
1+m
2+m
2 = 180°
5 = 180°
definition of supplementary angles
1=m
5
subtraction property of equality
4.
5. m
6.
7. r
1
5
s
definition of congruent angles
converse of the corresponding angles theorem
18. In the figure below, quadrilateral DACE is a parallelogram and
prove ABC is an isosceles triangle.
Statements
given
DE
definition of a parallelogram
DEC
ACB
If two parallel lines are cut by a transversal,
then corresponding angles are congruent.
DEC
ABC
given
ACB
ABC
AB
AC
ABC is an isosceles
triangle.
ABC. Determine the missing reason to
Reasons
Quadrilateral DACE is a
parallelogram.
AC
DEC
If two angles of a triangle are congruent, then
the sides opposite them are congruent.
definition of isosceles triangle
A. definition of isosceles angles
B. If two sides of a triangle are congruent, then the angles opposite them are congruent.
C. transitive property of angle congruence
D. If two parallel lines are cut by a transversal, then corresponding interior angles are congruent.
19. Is triangle DEF congruent to triangle XYZ?
Yes. Triangle DEF was reflected across its side FE and translated 8 units to the left
A. to create triangle XYZ.
Yes. Triangle DEF was reflected across its side DF and translated 8 units to the
B. left to create triangle XYZ.
Yes. Triangle DEF was reflected across its side FE and translated 2 units to the
C. left to create triangle XYZ.
D.
No. Triangle DEF is not congruent to triangle XYZ.
20. Keneda dropped her folder in the hallway and her geometry notes went everywhere. Sophia is helping her gather her
notes and picked up a piece of paper with the following diagram drawn on it.
Which of the following constructions would involve this diagram?
A. construction of a line perpendicular to
B. construction of a line parallel to
C. construction for copying
FDE
D. construction for copying AB
through point C
through point C
21. Which of the following reasons completes the proof below?
A. Side-Angle-Side
B. Side-Side-Side
C. Angle-Angle-Side
D. Angle-Side-Angle
Given: ABD
Prove: AED
Proof:
CBE
CDE
Statements
1.
ABD
Reasons
CBE Given
2.
AD
A
CE
C
Congruent Parts of
Congruent Triangles
3.
AB + BE = AE
CB + BD = CD
Segment Addition Postulate
4.
AB
BE
Congruent Parts of
Congruent Triangles
CB
BD
5. CB + BD = AE
Substitution Property
6. CD = AE
Substitution Property
7. CD
Definition of Congruency
8.
AE
AED
CDE
22. Triangle STU and triangle S'T'U' are given on the coordinate plane. Which sequence of transformations below shows
that triangle STU is similar to triangle S'T'U'?
Triangle STU was reflected about side SU, translated five units to the right and
nine units up, and dilated with a center of dilation at vertex S to create
A.
triangle S'T'U'.
Triangle STU was dilated with a center of dilation at vertex U, reflected about
side SU, and translated five units to the right and twelve units up to create
B.
triangle S'T'U'.
C.
Triangle STU is not similar to triangle S'T'U'.
Triangle STU was dilated with a center of dilation at vertex U, translated five units to
D. the right and twelve units up, and reflected about side TU to create triangle S'T'U'.
23. In the triangles below, x
y, e = f = 13 inches, and h = i = 16.25 inches. If g = 18.2
inches, what is the measure of j?
24. Given that the radius of Circle G is 13 cm, and the diameter of Circle H is 26 cm, what can be concluded about the
two circles?
A. not enough information is given
B. the circles are congruent
C. the circles are similar only
D. the circles are neither similar nor congruent
25. What is the rule for the transformation?
A. (x' , y') = (x , -y)
B. (x' , y') = (-x , y)
C. (x' , y') = (y , x)
D. (x' , y') = (-x , -y)
26. With the information given below, determine how triangle TUD can be shown to be similar to triangle SUY.
TU = 18 cm, DU = 21 cm, ST = 12 cm, YD = 14 cm
A. The triangles are similar by AA.
B. The triangles are not similar to each other.
C. The triangles are similar by SSS.
D. The triangles are similar by SAS.
27. If = 51° and n = 44 cm, what is the value of p to the nearest tenth of a centimeter?
28. The circle below has an area of 121
cm2. What is the area of the blue sector?
29. Which of the following transformations will never produce a congruent figure?
A. rotation
B. dilation
C. reflection
D. translation
30. Which of the following statements and reasons completes the proof below?
MKN, AAS
A. LKP
B. LNP
MPN, SAS
C. m LPK + m KPN = m LPN, Angle Addition Postulate
D.
PLM = 90° and
LMN = 90°, Definition of a rectangle
Given: Rectangle LMNP with diagonals LN and MP intersecting at point K.
Prove: LN MP
Proof:
Statements
Reasons
1. LMNP is a rectangle.
Definition of a rectangle
2. LMNP is a parallelogram. A rectangle is a parallelogram.
3. MN
PL
4. NP
NP
Opposite sides of a parallelogram are congruent.
Reflexive property of congruence
5. m LPN = 90°
m MNP = 90°
Definition of a rectangle
6. m LPN = m MNP
( LPN
MNP)
Substitution Property
7.
8. LN
MP
Corresponding parts of congruent triangles are congruent
31. The vertices of a quadrilateral are listed below.
I(-3,3), J(-2,2), K(-5,-1), L(-6,0)
Which of the following is the strongest classification that identifies this quadrilateral?
A. The quadrilateral is a rectangle.
B. The quadrilateral is a rhombus.
C. The quadrilateral is a square.
D. The quadrilateral is a trapezoid.
32. Which of the following transformations preserves the measures of the angles but changes the lengths of the sides of
the figure?
A. reflection
B. rotation
C. translation
D. dilation
33. If
= 40° and p = 28 cm, what is the value of m to the nearest tenth of a centimeter?
34. Which of the following illustrates constructing a bisector of an angle?
W.
X.
Y.
Z.
35. Which of the following sentences states a property or definition used in the construction of a perpendicular bisector?
A. Any point on the perpendicular bisector of a line segment is equidistant from each endpoint of the line segment.
B. Any two points equidistant from the midpoint of a line segment lie on its perpendicular bisector.
C. A line that bisects a line segment must be perpendicular to the line segment.
D. A line that intersects a line segment at an angle of 90° is parallel to the line segment.
36. Mick wants to design a new escalator for a company. The vertical distance from the first floor to the second floor is 28
feet. The escalator should make an angle of 35° with the ground. What will be the total length of the escalator to the
nearest foot?
37. A cereal company is creating new boxes for its product. In order to display the boxes, the stores they sell to require
that the boxes be 11.5 inches high and no longer than 8.4 inches. The printing department requires exactly
272.8 square inches of space in order to use the planned design that covers the box. If the company wishes to maximize
the length of the box, then what should be the width of the box?
38. In the circle, RV and SW are chords which intersect at point T. If ST = 4 ft, TV = 8 ft, and
TW = 12 ft, what is the length of RT?
39. A 60-inch tall boy is standing next to a 40-foot tall building. The boy casts a shadow that is 24 inches long. What is
the length of the building's shadow?
40. The vertices of a quadrilateral are listed below.
A(6,-7), B(-7,-7), C(-12,7), D(1,7)
Which of the following is the strongest classification that identifies this quadrilateral?
A. The quadrilateral is a square.
B. The quadrilateral is a rectangle.
C. The quadrilateral is a rhombus.
D. The quadrilateral is a parallelogram.
41. If
L
N, what else is needed to prove KLM
A. LK
NP
B. LM
NM
C. LM
PM
D. KM
PM
PNM using the Angle-Side-Angle rule?
42. Howard is standing 97 yards from the bottom of a water reservoir. He estimates that
the angle of elevation to the top of the water reservoir is about 60°. How far is Howard
from the top of the water reservoir?
43. Which of the following illustrates constructing a congruent angle?
W.
X.
Y.
Z.
44. If m
= 84°, what is the value of x?
45. The local police department is building a new isolation cell and is planning to make one wall of the cell out of bulletresistant glass. The cost of the glass is $43.92 per square foot. The total cost for the glass that is being made will be
$3,206.16. What is the size of the bullet-resistant glass pane that the department ordered?
46. Cassie wants to determine the length of the shadow that a 20-foot tall telephone pole casts without measuring it. If
Cassie's mailbox, which is 42 inches in height, casts a shadow that is 31.5 inches in length, how long is the shadow that
the telephone pole casts?
47. The measure of ABC is 135°. The length of radius BA is 6 centimeters. What is the area of
the shaded, larger sector?
48. Jolie is constructing the following triangles and draws VR parallel to ST. According to
the SAS theorem, which of the following needs to be true to show VRT
STR?
A. VR
B.
ST and
RVT
C. TV
RS
D. VR
ST
RVT
SRT
TSR
49. Jimmy is designing a doghouse for his pet. He wants to determine the amount of overhang
of the roof so that the shadow of the noonday sun reaches the bottom of the 6 foot wall during
the summer months. The highest angle of the sun during the summer months is 75°. How much
overhang does Jimmy need to provide for this purpose?
50. Mr. Jameson is walking toward his nine-story hotel and stops to look up to the top of the
building. The angle of elevation to the top of the hotel is 55°. If the height of the hotel is 99
feet, about how far away is Mr. Jameson from the hotel?
51. Jill and Marcy go to an ice cream store where they have the option of getting a smoothie in
either a cylindrical or rectangular container. The cylinder has a height of 7 cm and a radius of 6 cm. The rectangular
container has a height of 7 cm, a length of 6 cm, and a width of 7 cm. Jill purchased the cylindrical container and Marcy
purchased the rectangular container. Who got the larger smoothie, and what was its volume?
52. Triangle FGH is similar to JKM. If f = 16.2 cm, g = 18.63 cm, h =
29.16 cm, and k = 10.35 cm, what is the measure of m?
53. If X = 18 yards, Y = 80 yards, and Z = 82 yards, what is the sine of
B?
54. In the dilation shown, the dark-colored figure represents the original image and the lightcolored figure represents the resulting image. What is the scale factor for this dilation?
55. Wally wants to determine the height of a statue that casts a 88-inch shadow by comparing it to his own height and
shadow length. If Wally, who is 71 inches tall, casts a shadow that is 44 inches in length, what is the height of the statue?
56. What are the coordinates of E' if E'F'G'H' is a reflection of EFGH across the y-axis?
A. (-6 , -3)
B. (-3 , 6)
C. (-3 , -6)
D. (3 , -6)
57. What is the rule for a reflection across the x-axis followed by a translation 8 units to the right and 2 units down?
A. (x' , y') = (x + 8 , -y - 2)
B. (x' , y') = (x - 8 , -y + 2)
C. (x' , y') = (-x + 8 , y - 2)
D. (x' , y') = (-x - 8 , y + 2)
58. The vertices of a rectangle are listed below. What is the area of the rectangle?
M(-1, -6), N(-1, -3), O(5, -3), P(5, -6)
59. Which of the following shows a dilation of the figure shown above from a point that does
not lie on one of the sides of the figure?
W.
X.
Y.
Z.
60. The vertices of a triangle are listed below. Which of the following correctly classifies the triangle?
A. The triangle is an acute equilateral triangle.
B. The triangle is a right scalene triangle.
C. The triangle is an acute isosceles triangle.
D. The triangle is an obtuse scalene triangle.
61. The vertices of a triangle are listed below. What is the area of the triangle?
T(5, 6), U(1, -2), V(-1, 0)