S.R.T.T 6.1ReadyNote: For questions 1 6 the scalefactor r.l.'ill be provided. Hor,;ever,students shouid also find the missingside Iengths, though those valr.res willnol he nrovided helc
1. Scale Factor: 2
2. Scale Factor: 3
3. Scale Factor: 44. Scale Factor: 1.5
5. Scale Factor: 5
6. Scale Factor: 3
Set:7. Center: Fran
Tool: CameraB. Center: Technician
Tool: Zcom9. Center: Melanie's eye
Tool: Thumb10. Center: Vanishing Point
Tool: Cornputer11. Center: Finger on one end
of rubber bandTool: rubber bands
12. Center: Top left corner ofcopy machine glass
Tool: Copy Vachine
Go
1J.
74.
I ..).
16.17.
18.
Quadratic: The seconddiffercrrce is 2.
Exponential: Doubles as xincreases by 1, and shape ofthe graph.
Quadratic: x2Linear: 7x
Quadratic: Shape ofthegraphLinear: Slope of 2
S.BJ{.6-ZReady1. a
7.. b
3.e4.f(r
6.d
Modul e 6: Similarity & Right TriangleTrigonometry
Answer Key
Set7.
11. Ratio: lC t ntir
1 2. Ratio: 2
b.
o 2013\ Il R iglrts Resen erl.
Nt\l',}r-rC..
25
13. Center: G
Ratio: I
14. Center: ARatio: l
Go
15. 90" Clocklt'ise rotationE
A,t\t\| ,tr.t//.r'rc
A//\,/ \ ,, r',-. \ (;
16. ReflectionL
.,,;E
Mathen'ratics V ision Pro iectlN4 V PFol irrdir idrrrrl lntl clasitrrortt ttsc
A "'"'1*"1'"''"""\ /"t'+17. Translation: (x+7,1 f l)
18. Dilation
5&T16.3DDnlltl
l. x: l)) --A
3.x=164.c=155.b=726. a-14
8. b=17
A r-/"
aO
l\lotlrrlL. 6: Srrrril,rlitl,\ RigltlSetNotc: Btlo,,r, proitl.s andcori n lerc\it t)lpIes it |e nte|r.lv a s.r rrr1lltol possible:tnsivers.
10. False. A right tr-iangle wrtlrsides 3-4-5 is not sinrrlar tcr
a right triangle lvith sicles5,12-13.
11. Trlre. Regr.rl;rr polygons ivillharze the sante interior- angleme:r.sufes Ilo lrattef thcsizr,, f ltcrt'lotL' ln.tkir'tg Iltr'ltl:rllsinrilar'.
[2. Trtre. Tire object has hacl a
r']clrtive tiil:tion. ll yorr
co n nect cor|c's oon cl i n g
points, they all cross at thecenter of dilation. Thislll es('l Vr's r llllr' lni-.lSttI'r'l''"' ''""'-'_ ,,'
and therefore the objectsare sinlilar.
13. False. You may notice,
:!4N : M',N', horveverLM : L'M'. Because of thiswe know these sides clo nolshare the sarne scale factor.
i4 q0 coirntrr-clur.kwi>crotation :rround point A,
also a u dilation occurreciwith center A.
15. 9 0' cou n tei-clockrnriserotation has occurred as..,.-ll -- ^ r,lil-F;^,,tvrlt .l-\ d - Llttdilull,
This -shape has beenreflected then rotated.
This shap.e has beenle[]or Ierl vcrt ic.rllv thr'ltr,\t rr ^rl Oft r.n"-,-l ^,'int A
17.
GoNote; I;or questions 1B - 2 1 studentsa|e asked to provlcle three equivalentratlos. lvlirny are possible, and 3 havebeen proviciecl below.le r0 - l0 _ | l.
6 :J',S I 4 5
M " -
zt|. - -
L6
9 r_t 6_2aanQ4
;'t- rs'a- r-
21 2) _ 1 d 2l7 d v5s'i5i
€) 2013 Mathematics Vision ProiectlMVPAll Riehts Reserved. For indir idLr.il rrnd classroom Llse.
'f lia ngle 'l'rigonoin ctt-yS.R.T,T 6.4
ReLrcly
1. LJ
2. 1
1 TiJ, V LJ
43- ctt.J. JV Z''6. 10
5cfNote: Fol questions 7 - 8 slrrdents irreasl<td to plovicle thlee erqLrivalentratios. Nliin-l are possiirle, and 3 hai'ebcen plovidcd belorv.1 .1 _d b_e d_c' n-7';-,t'; h
o BA- AC_,;-
9. n= 2.6
j
CB ]1 DE .\,18C - A.IED
12. AB II XY il PQ
ACPQ-LCYX-CBA
13. GF lt rH ,AJ!H - LIGF
1.4. LH lt GJ ,LFLH - AFGJ
Ht.ll FC ,AJHr- AJFG
GrL
l5
CTI}C BI. -
FI)BD'm - 6
l0
11
Anslve-r'Kcy
,4.'5
;
:a
S.RJ.T 6.5Rearly1. 5
?.63. 26+. /.:)5. ).2
6.87. A-E , Rcttio 1:2
B-C,Rcttto 1:3D-F , Rcttict L.4
Set8: a =
h-
x=
z=
I26
T2
60'60'40"
B
45
10B
9
J/
g0'J.)
9; a=h-
,l-
a-
7.-
Go1n
11
74.r=
72
152
4
4
1516.
17.
i ll.
x=21^._14
x: 10
Module 6:
Ready1.92. 10.52/"4.35. +7.56.101
7.9B. 349. 6710. -2811. -21.
1"2. 3
Similarity & Right TriaS.R.T.T 6.6
Set13. [s,4J14. (2 ,2)is. {8, o.sl16. [1.s , 1.s]17. (6 ,e)18. [0.5 , -0.s]
Ie. 14 , -2)20. (4.s ,-1)21. {-1 ,4)22. {s ,2)23. They are proportional to
one anotller.24 Yes. as lonp as there is one
pair of parallel lines, youcan find proportionalrelationships.
Co
25. /.J
26. 6
S.R.T.T 6.7Ready1.A-C,AAA
B=G,ASAD - H,SSSE:F,AAA
Set2.b3.b+-e(-6.f7.lr
B. Horinzotrtal: 13
Vertical: 4.62
9. Horizontal: 3.9
Diagonal: 6.24
ngle TrigonometryCa
14. 7
11. 9.6
12. 12,1,713. L4,281+.21,3215. 6,12
s.R.T.T 68Ready1. a = 36.82"
n-4
2. a= 64"n = +r/3
3. a= 45". t^n = o1r'z
4. a = 55.01"n = ^ft+g
5. a = 21,.8"t^^n=\zY
6. a = 22.62'n=1,2
Set7a. 0.496b. 0.868c. r./5d. 0.86e. 0.496f. 4.444
8a. 4.943b.0.333c.0.353d.0.333e. 0.943f.2.833
9a.4.707b.0.707c. 1
d.4.707e. A.707f. 1
10a. 0.8b. 0.6c. 0.75d. 0.6e. 0.8c 1 aaaI. I.JJJ
Ail
21Answer KeY
GA
Lra. f(x):(x* 5)(r+a)b (-s,01, (-4,01c. [0, 20]
12a. g(x): (x * 5)(x - 3)b [-s,0], [3,0]c. [0, -15)
13a. h(x) : (x + 7)(x - 7)b. [7,0],{-7,a)c. [0, -a9j
14a. r(x) : (x - 3)(x - 10)b. [3, 0], [10,0]c. [0, 30]
ISa. f{x) = (x + 1A}2
b. [-10,0]c. [0, 100]
1 ba. g(r) - (x - 12)U + a)b. (12, 0l , i-4 , 0lc. [0 , -a8)
17a. h(x): (x + B)2
b. t-8,01c. [0,64)
18a. ft(x) -- (x + 6)(x - 6)b (-6,01 , t6, olc. [0, -36J
19a. p(x) : (x - 6)G + a)b. [6,0],t-4,01c. (0 , -Za)
S.R..T.T 6.9Ready1.Bx-10=x+11-x -x1- _14, 11
+10 +10
+7 :7x=3
+Zx +2x
5x+9=44-9 -95r-35:5. +5
a- |
3r*9=44-2x
Subtracti onP.O.E
AdditionP,O.E
DivisionP.O.E
DivisionP,O.E
S u btractionP.O.E
DivisionP.O.E
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28Modr-rle 6:
3.
Similarity & Right Triangle Trigonometry
I Ltstification
M ultiplicationP.O.E
DivisionP.O.E
Jttstificatio n
MultiplicationP.O.E
x$ xJ3r=45+3 :3
x=15
"2I "21,x=14
a- 15uc. ;
l- 15u,frr:-' 17
fl:
'e. GlvenJ-:
17
8a. 1A
hl n'12
.1L.=
\z I0_te. GivenF1
'J2
9. False, cos(,A) = --lsrn (6J
10. True, Because 90" - A = B
11. True. tan(,4) ' cos(A) :o.A*9:sin(4)AHH
UO
12. Slope = 1
O 2013 Mathematics Vision ProiectlMVPAll Rights Reserved. For individudl and classroom use.
Set5a. Given
h:*' 5
r!', 5
o. :3
^4-5f. 1
5
13
c. Given
^1213
[.:13
N'h\,D
l -)
f.{[r \.
J
A
IL
B
15
16
1.7
13. Slope = -l
14. Slope =
Sider 8Slope = n
Side: 4Slope = - z
Side: 7
Slope = - 1
s.R.T.T 6.10Ready1.
Set4a. 23.58"b. 66.42"c'.9.1.7
Answer Key5a.70'D. t5/./Ic. 82.42
6a. 40"b. 81.04c. 1.48.97
7a.70"b.2.91.c. 8.51
UOo- r
zhv
2
C,:v
AYz
z€y
9a. I!2L1
'J2
^1;l
l2^l
.12
{1.JZ
o 4F'"1." / (o
lO: €?,
lal
r-C.1/J.l 1
r:v3
9. 60"h. 30'
s.R.T.T 6.11ReadyI nlL. / .J
2. 6.433. 12.54. Upper: 6,Lower: 45.356.9
Set7. A--19.1.9"
B = 70.81"
BC'= V35
8" A=30"AC = 17.32BC=10
11.
Module 6: Similarity & Right Tria
9. B=65'AC = 18.13BC = 8.45
ln A _ -o
AB = 10.04BC = 0.875
A=50'AB = 4.667BC = 3.575
A = 51.34"B = 38.66"AB = 6.403
'B5 J". l -1"
A 49..1'
12.
13
L+.
1rI.r.
B,10.6"
16.A J5.57'
4r1.13"B1t1
17.
Rt8.bs'
36.87"
18.,1 1.1 9 1"
'B15 07"
ngle Trigonometry19. sin(A) : cos(B)
tan(B) : *:,8cos(,4) : sin (B)a2+b2=c2stn2(A) t cosz(A):1
20. 37 in
lL / L /O nOnZOntal iellgtn.4.76' incline
1.16"
22. Angle 22.62"
il
13+.76"
Module 6 OuizPqrt Il.o2.d3.a+.e
Part II6.
7.
B. x = 2.699. x = 1.65810.4.511. x=68'
,, - o?o,,/ - '-- 1 1)a
AII
29Answer KeY
Module 6 LestPart I1.. f2.c
4.cf,. I
6.b
7. cB.a9.e10. b
11. d12. f
Part I13. C = 3.61
A - 56.3 l'B : 123.69"
14. x = 3.47
v = B'06A = 60.26"B = 29.74"
Pqrt III15. Sample Proof: We know'that the sum oI the interiorangles af AABC equals 180'.Since zACB : 90'andtABC :30'we knorr,r thattCAB = 180'- 90'- 30" : 60".
Therefore, AABC has anglemeasures 30", 60", and 90'.
By construction we knorvthal zCAD : 60o and similarly,zADC : 90', and using theinterior angle sums, we l<now
that zACD : 30". ThereforeA,4DC has angle rreasures 30' ,
60' , and 90".Finally, by construction rve
knowthat zACD * LDCB =90'. We already showed thatIACD :30', so tDCB : 64".Tl.ris proves that ADBC liasangle rneasures of 30' , 60o ,
and 90o as well.Therefore,
AACB-ACDB-AADC,
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