Name _________________ Date _____ Period ___ _

Unit 6 Study Guide \ ll., I ')

1. If llKLJ ~ llVWU, find the value of x and write the scale factor of the smaller to the larger triangle. Keep your answer in simplified fraction form.

2. Given: llMLP~llMNO and MP = 10.5 What is the length of OP?

'l. l L U

I K 4x-23

x=_\_l __

4 k= __ s;-__ _

W 20 V 1

1-{~- ~ ""~.:l.. - -";). 4'1- -~3

Y.l ~~-:l~):: ~l ~,d·-~)

\ l.i)C. - -= l-o~ + l'O

~1,. ::. lo"'l... )(.-=17

3. Given that the following triangles are similar, Part A write the similarity statement

M

N 0 12 ""

,;1: '•-h L_J \:' q L N 12 o I

ll.. }C

9 -== \o .,S-

'1x. -= l:t{, ~ -= ,4

\4 - \o.~ :::

Part B Write the scale factor of the s~ r to the larger triangle.

E Na 10~ ..

D F

25 ----. K

L

4. Choose the correct justification to prove the two triangles below are similar.

H Statement AA SAS Similarity Similarity

9

M 86° 6 T

15 6 D r/ - = -and LM = LQ 20 8

15 6 9

s -=-=-20 8 12 15 9 20 = 12 and LM = LQ D D

.12 LM = LQ and LT = LW ri D

w 8 Q

:2.. k = s;

sss NOT Similarity Similar

D D

rl D

i 0 [ j

3

I ,. l I }. l 5. Given that ~FGH is similar to ~FED, calculate GH 6.

to the nearest httndr edths place. +-~+~s

6 F

The community park has a swimming pool enclosed by a regular fence for sunbathing measured at 112 feet by 63 feet. The people in the community would like a walkway for the children going around the pool. The pool is similar to the fence, using a scale factor of~- What is the

7 distance around the pool they would need in order to make the walkway?

"~ \l~+~'l 4l\"l..+t.1-= 3,~D. ~-1 -~·[ }· l J.1 ::. \~. -;t_~ \oo +t I\ 2..

D ~ ,~. ")S" 7: '\(

d°3>~ :: 7 l. S"" 1..;\.

t. JLi-~ r, 9 f", c=J,~ ~::t. +-\ i +-"3 2 + \ e =- I oo .2. :;l.

)£. -= i . ' q ~c.. . . . I~

7. A square ABCD with vertices A(-7,-4),B(-4,-3),C(-3,-6), and D(-6,-7). Transform ABCD so thatA'B'C'D' dilates based on the scale factor of 2. lV\ ..._ \ h l c- c!· cA<.-s. 'b s.~4.\ , -9 "-L--h.r. '\"''"' •r- . "' ...

A \

\ \ ,.,...~ C ,,

A' ( -\~ -~ )

B' ( -~ - (c )

C' ( - l,, - \). )

D' ( -\ -14 )

32.

\Oo

8. Triangle DEF with vertices D(2,2), E(2,6), and F(6,2) using a scale factor of k = i and centered at P(-6,2)

t:'

' E ' ' .....

" ..... V o• F' ID r-

What is y-coordinate of D'?

9. Which words correctly complete the statement below?

L\PQR is dilated with the center of dilation at the origh1 and a

scale factor of 2 to obtain L\P'Q'R'. The triangles' corresponding

angles are_• __ and their corresponding sides are ___ _,

therefore, the triangles are __ _

@ congruent; proportional; similar b. congruent;congruent;congruent c. proportional; proportional; similar d. proportional; congruent; congruent

10. Given L\GHI: G(4, 4) H(6, 8), /(8, 4). Use the graph to'the left to transform the figure using the scale factor of½ centered at X(6,2). State they-coordinate of/'.

. .L

11' I 'll:

ll.l-1 l~l~ 11. In the diagram, JKLM ~ABCD, find the values of x, y, and z.

l 6 :,.. L K

15

M

?, \S" '/.. -q~-::,. 1:2..

'h. -= 3\p

--t, -=-9

J l

' A

B,). y

0------c :1 'i 20

-

x=I 9

y = I S?

z=1 70

12.MBC with A(0. 0), 8(8, 6), and C(B, 0) . Graph and state the coordinates after: i:

3 3 l)(x,y) ~( 2x , 2y) 2) reflection in the line x = 2

A': ( 1-f

B': ( - '6

6 )

9 ) C,'

C': ( - D )

13. Determine the coordinates of point T if point Tis located on RS such that the ratio of RT: TS is 3: 1. Use the following coordinates: R(-2, 5) and S(2, -3). y

g 8 1 61, -

' 4 3

\

1

.g -a .7 .. -5 -4 -3 -2 ., • ' ·1 l'T ·2 .3 -4 -5 -6 •7 ·8 •t

ti : 1..\/4 I u "-~-\-

\} : ~/4 =- """':+- {

n " 3 • & 6 7 9 X

' s

'" V I'.. .,. ,

-.... w 'r--.. V

I"- _..I'"

I" I/

' V ,., <..

/ "' I\ f\ fl' c:,

14. Point P is located on XY such that the ratio of XP: PY i~ 3. lfthe coordinates of XYare X(-3, -4) and Y(S, 0), what is the

x-coordinate of point f? II 8 7 8 5 4 3 2 1 I 'i

-9 -8 •7 ,t •5 -4 -3 •2 •I C 1 2 3...,. ....- 6 7 • g •I ...... ... ·2 .... 1, 1

,,,, ,-

X

X ·S 0 --6 .7 -8 .9

I t

6

C.

L- 1, -4) 4 (-1~ ,-Y

+I~ t- l\c,1 ts-'ls-

\/<;;; or 0 .

15. Point O is located on a line segment MN where M(2, -3) and N(7,2). Find the coordinates of 0 if O partitions the directed line segment MN in a ratio of 2: 3. ·

y

9 a 7 6 s • 3 2

I/ 1 V -9 -I •7 ,t •5 -I -3 •2 •I C 1 2 30 ll_S 6 .,

/ " -2 V ·3 M "" .5 -6 •7 ·6 .g

tt ~ ~/i; Iv-,:- +

'V ! ~/ S" ::. \ '-'-: t

C -

;iJ

'C 9 X -

For exercises #17 - 18, find the missing length indicated. Make sure to leave your answer in simplest radical form.

/1\ 12 8

16. Given the points A(2,4) and 8(8,10), find the ~- coordinate/ of the point Don the directed line

segment AB in the ratio 5: 1.

y • !/" 9 V a

7 I/ l

I/ '" 6 / 5 / • " 3 I -

2 I

.g 4 •7 ,t ·5 -4 •3 -2 . , 1 1 2 3 • 5 6 1 8 9 ., X

·2 ·3 -4 .5 -6 •7 -a .9

7

18.

7

7 f.. -;::.-

)( .;)_~

'il l L\

19. Four streets in a town are illustrated in the accompanying diagram. If the distance of Maple Street from M to Pis 12 miles and the distance of Maple Street from E to M is 10 miles, find the

~distance of Poplar Street, in miles. Round to the neclr st tenth.

Maple

- 'I--- - -X 1:l. X~:::. ~lllLf

20. To estimate the height of the totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which is the best estimate for the height of the totem pole?

d- 3 1 · -=, x .,}.)( ::. 9

v:, -:. 4 -<:; '

For exercises #21- 24, determine whether the triangles are congruent by AA~, SSS~, SAS~ or not similar. If the triangles are similar, provide the similarity statement. If the triangles are not similar, write n/a.

21. L 22. y

23.

. c

K

E

= 0 -114;:... . . ./\,,

~q RYN - ~o -l\4.l. .. D ------A 6'1 11.25 .;t. - = 0 -~ la

.9-. = o.~ 11-~

: l) .(l

Similar By: _S_-A_~_-. __ _ 1i"imilar By: - ~-t~---

llPKM ~ b. LQM

'..-- - -----7 B p

Similar By: _ N__,/.__A __ _ ACAB~ ____ _

24.

s

Afl.YN,.., bf\t>E"

F

Similar By: ---'-'f,'-'-~-'------

1:iPAS ,:,, _b.~f ....... f\_C... __

25. QRST is transformed to create Q'R'S'T'. Determine the scale factor of the dilation performed.

26. Given that 6.QRS is similar to 6. TRU, what is the perimeter of trapezoid QTUS?

J 9 a

. 7

6 s ' 3 - -

J ' 2 I I ""' "

.g .. . 7_ . ·5 -4 -3 -2 .:1 C I 2 3 • S 6 J J •I , I -t

' J -3 , , -4

i ' -s I , -6

J ' .7 , , -a s T ·9

27.Given: !.!!... = Ko NO MO

Prove: Lf = LN

J

statements JO KO

l. s NO= MO S

2. A LKOJ LMON

3. fl]KO~llNMO

4. L]~LN

A. If two lines are cut by a transversal, alternate interior angles are

congruent.

B. Definition of vertical angles

7 a

C. If two lines are cut by a transversal, corresponding angles are congruent.

9 15

_______ ___. s 14 I '-t

"J.Ji__ ){ 1 ':I, - ,4

1. T. 2. ~-3. b.

4. ~-D. SAS Similarity

E. AA Similarity

F. SSS Similarity

l "1- =J.'6 ~='-f

N

5:S

Reasons

G. In similar triangles, corresponding angles are congruent

H. In similar triangles, corresponding sides are proportional.

I. Given

s

28. Given: ND II AR Prove: flNDZ~MRZ

D

statements 1. a... 2. K. 3. q. 4. \ .

a. ND II RA

d. Triangle NDZ is congruent to triangle Z RA

g. LNZD = LAZR

j. ND= AR

29. Given: MQ II OP Prove: MN = QN

PN ON

statements 1. MQ IIQP

2. LQMN ::: LOPN

3. c. 4. !!.QMN~l!.OPN

5. MN QN -=-PN ON

3

Reasons 1. Given

2. Corresponding Angles

3. Reflexive Property

4. AA Similarity

b. LNZD = LARZ c. LAND = LRAZ

e. ND II AR

h. Definition of vertical angles

k. LAND = LZAR

1. Give~

f. Corresponding parts of congruent triangles are congruent

i. Triangle N DZ is congruent to triangle ARZ

I. ND= DZ AR RZ

Reasons

2. Definition of Alternate Interior Angles

3. Vertical angles are congruent

4. AA~

5.

Which statement completes StepK ofthe proof?

a. LMQN = LOPN

c. LMNQ = LPNO

b. LMNQ = LONP

d. LNMQ = LNOP