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

O 2013 Mathematics Vision ProiectlMVPRights Reserved. For individual and clasiroont use.

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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