Castle Learning Assignment

Christmas Assignment
Teacher: Mrs. BIES
Name:
--------------------------------
This assignment is due by Friday, January 9, 2015. All work needs to be put in this packet AND entered
into Castle Learning before midnight January 8, 2015. Failure to show work or enter answers into Castle
Learning, will result in the deduction of 20 points from your score.
A rocket car on the Bonneville Salt Flats is traveling !_Express the product (2x- 1)(3x + 4) as a trinomial:
at a rate of 640 miles per hour. How much time
would it take for the car to travel384 miles at this
1. 5x2 + 9x -4
rate?
2. 5x-4
3. 6x2 -5x-4
1. 36 minutes
3. 256 minutes
4. 6x2 + 5x-4
2. 245 minutes 4.1.7 hours
t)
In the diagram below, AD bisects LABC. Find x,
m LABD, m LDBC and m LABC.
\If a girl 1.2 meters tall casts a shadow 2 meters long,
jhow many meters tall is a tree that casts a shadow 75
lmetern
1:::
fue
srunet~e?
@
jin the accompanying diagram of isosceles triangle
IABC, AB :: AC, and exterior angle ACD = 110°.
!What ism LBAC?
A
8
c
The value of x is
11(V
mLABD=
B
mLDBC=
\Answer:
mLABC='
c
D
Christmas Assignment
~
In the accompanying diagram of right triangle ABC, !In the accompanying diagram of !!.BCD, m L C = 70,
CD is the altitude to hypotenuse AB. If AC = 9 and 1m L CDE = 130, and side BD is extended to A and
AB = 27, find AD.
c
c
('
A
/
D
1 + - - - - - - 27
~./..
--------""1
lA
Answer: AD=
B
D
E
lmLCBA='
~
In the diagram below, !lRST is a 3-4-5 right triangle.
jA cake recipe calls for 1.5 cups of milk and 3 cups of
The altitude, h, to the hypotenuse has been drawn.
lflour. Seth made a mistake and used 5 cups of flour.
Determine the length of h.
jHow many cups of milk should he use to keep the
'proportions correct?
T
11.1.75
Answer: h =
What is the value of x in the equation 4(2x + I) = 27
+ 3(2x- 5)?
I.
2.
21
9
3.
7.!..
4.
4
I
2
I
3.2.25
4.2.5
Christmas Assignment
In the accompanying diagram,
CD II Eft, AB is a transversal, m L DGH = 2x, and m L FHB = Sx - 51.
c
D
E
F
Find the measure, in degrees, of L BHE.
Answer:
In the accompanying diagram, parallel lines
Y, and m L FYD = 123.
F
mLAXY=
AB and CD are intersected by transversal EF at points X and
Christmas Assignment
In the diagram below, MBC ~ !:JJEF, DE= 4, AB = x, AC = x + 2, and DF = x + 6. Detennine the length of
AB·
D
A
E
c
F
Answer:AB=
In the diagram below of MBC, DE is a midsegment of MBC, DE= 7, AB = 10, and BC = 13. Find the
perimeter of MBC.
8
Answer:
Christmas Assignment
pV
The accompanying diagram shows quadrilateral
BRON, with diagonals NR and BO, which bisect
each other at X.
ILh
I"
10Rgu:1' T
!In the diagram of right triangle RST: SW is an
jaltitude drawn to RT which is the hypotenuse, ST=
112, RW= 10, and WT=x.
Prove: ilBNX::: ilOR.X
The following is a list of possible statements and
reasons that could be used in the proof.
l(a) x
units.
=
jCb) To the nearest integer, SW=
A. SAS: SAS
units.
}0
B. AAS:AAS
C ASA:ASA
D. NR and BO are diagonals
E. <t..BXN:: <t..OXR
F. <t..BNO:: <t..ORB
G. A segment bisector divides a line segment into two
congruent line segments.
II:/3/Ic
B
A
H. An angle bisector divides an angle into two congruent
angles.
Figure 2
In the proof below, fill in the letter of the appropriate
statement or reason from the list above.
In the diagram of rectangle ABCD, AC = 22 and
mLCAB=24.
Statements
l.BRON is a quadrilateral
Reasons
1. Given
~.Given
2. ·~~······ ·:
3. NR and BO bisect each 3. Given
other.
1
4.NX:XR
ft. ..... j
5.0X:BX
5. [
J
6.
i
7.1lBNX: ilORX
6. Two intersecting lines
form congruent vertical
angles.
7.
··~-····
(c) Using the results from parts (a) and (b), the area
ofABCDis
square units.
Christmas Assignment
15 ft
iNotdraififl to scale)
Figure 3
The accompanying diagram represents a tree. To the nearest tenth of a foot, the height of the tree is ·
feet.
Old Tent
15ft
Figure 4
The Rivera family bought a new tent for camping. Their old tent had equal sides of l 0 feet and a floor width
of 15 feet, as shown in the accompanying diagram.
Ifthe new tent is similar in shape to the old tent and has equal sides of 16 feet, the floor of the new tent is
feet wide.
Christmas Assignment
~ill
in the missing statements and reasons for the proof using the list provided below.
Given: D is the midpoint of CB
~ADC=: -«ADB
A
D
=
Prove: ~ C
~B
The list of statements and reasons below form pieces of proof.
List of Statements and Reasons
Sl. SAS=:SAS
S2. AD=:AD
S3. A midpoint divides a line segment into two conguent line
segments.
S4. CPCI'C
Part of the formal proof is shown below. Complete the proof by filling in the labels of the missing
statements and reasons from the list above (SI, S2, S3, S4).
Statements
Reasons
I. Given
I. D is the midpoint of CB
2. Given
2.
~ADC =:
-«ADB
3. CD=:DB
4.
'L~····
....
6. i:!.ACD'iS i:!.ABD
7.
~C=~B
3.
:·····~~·]
4. Reflexive Property
6.
.l
7. :
V~NV~h~V~'
VhhVVhNYh
Christmas Assignment
~
In the diagram below of MCD, Eisa point on AD 1In the accompanying diagram, triangle A is similar to
and B is a point on AC, such that EB II DC. If AE =!triangle B.
Triangle B
Triang!o A
c
;\,,
i ,,
.I ""'
A
'0
rind
'A
3
the value of n.
in=
0
Answer:EB=
If 10 cubic centimeters of blood contains 1.2 grams
of hemoglobin, how many grams of hemoglobin
would 35 cubic centimeters of the same blood
contain?
1. 4.2
2. 42
3. 29.2
4. 291.7
Solve for x: 6(x- 2)- 4x = 16
1. 2
2. 7
3. 12
4. 14
rI
I
A
c
,
1
Rgure 5
!In the diagram of 11CAT, W is a point on AC and G
lis a point on TC such that WG is parallel to AT· TG =
GC = x- 1, CW = x + 5, and WA = 2x + 6.
lx,
Christmas Assignment
~
What is the negative value of x that satisfies the
equation 2x2 + Sx - 3 = 0?
rLAOF.
1. -1
AB, CD, and EF
EF and m LAOE = 32, find
lin the accompanying diagram,
!intersect at 0. If CD ..l
1
2
3. -3
2
4. - 3
2. - -
A
B
In the accompanying diagram, line m is parallel to
line p, line tis a transversal, m La= 3x + 12, and
m L b = 2x + 13. Find the value ofx.
f
a/'
I
t
m~•-----------+~----------••
I
I
x=
(nswer: m LAOF= ...................
~
IJiB and Cfj intersect at E. If m L AEC = Sx - 20 and
~m L BED= x
+ 50, find, in degrees, m L CEB.
~Answer:
~
· · · · · · ·~· ~
jTriangle XYZ is similar to triangle RST with LX~
LS. If XY = 4, RS = 12, ST = 18, and
TR = 24, find the length of side yz.
!LR and LY ~
I
!Answer: YX = •
I
Christmas Assignment
¥D
Ron and Francine are building a ramp for performing !As seen in the accompanying diagram, a person can
skateboard stunts, as shown in the accompanying
!travel from New York City to Buffalo by going north
!170 miles to Albany and then west 280 miles to
diagram. The ramp is 7 feet long and 3 feet high.
!Buffalo.
What is the measure of the angle, x, that the ramp
!
makes with the ground, to the nearest tenth ofa
I
Buff..,a_lo___2_Bo_m_H_.e_s__AJ..,.··.,oany
deg.-ee?
170 miles
3ft
]
~~u-~~~"'"'M~--"''"~
Answer:
0
New York City
!a If an engineer wants to design a highway to connect
!New York City directly to Buffalo, at what angle, x,
!would she need to build the highway? Find the angle
Ito the nearest degree.
!Answer:
0
Jb To the nearest mile, how many miles would be
!saved by traveling directly from New York City to
!Buffalo rather than by traveling first to Albany and
lthen to Buffalo?
rnswer:
miles
Christmas Assignment
~ill
~~
in the missing statements and reasons for the
proof using the list of possible statements and reasons~Triangle RST is similar to LUTZ with RS = 3 inches
~and XY = 2 inches. If the area of !lRST is 27 square
provided below.
hnches, determine and state the area of !lXYZ, in
Given: ABCD is a parallelogram, BFE,CDE,AFD ~square inches.
B
~--------------------~
~
C
E
Prove: AF x EF
=
DF x BF
The following list of statements and reasons are
possible pieces of the formal proof.
Figure 6
List of Possible Statements and Reasons
--
Sl. AF = BF
DF EF
S2. !:::.BAF - MDF
S3: The product of the means is equal to the
product of the extremes.
S4: -«.BFA==: -«.DFE
S5: Parallel lines cut by a transversal create
congruent alternate interior angles.
1In the accompanying figure, two lines intersect,
~m L 3 = 6t + 30, and m L 2 = 8t- 60. The number of
Idegrees in m
II
Part of the proof is shown below. Complete the
formal proof by entering the labels of the missing
i
statements and reasons using the list above (S I
through S5). A statement or reason may be used morel
than once.
~
;
Statements
Reasons
I. ABCD is a parallelogram, I. Given
BFE,CDE,AFD
12. Two intersecting lines
2.
~orm congruent vertical
!angles.
3. -«.BAF ==: -«.FDE
~.
4.
'
' ....... ~J
!4. AA- AA
15. Corresponding parts
...'
.
5.
-
k). AFxEF = DFxBF
l<>f similar triangles are in
!Proportion.
16.
·-
l
L 4 is