CC Geometry Midterm Review Questions

Mame: Date:

1. Using the diagram, identify the dashed line segment.

A. median

B. altitude

(c ) angle bisector

D. perpendicular bisector

2. The diagram shows a method for constructing

A. a median in a triangle

B. an angle bisector in a triangle

(d) an altitude of a triangle

D. the bisector of the base

3. The diagram show how to construct

A. an altitude of a triangle

B. an equilateral triangle

C. an orthocenter

( D ) a centroid

In the figure, k || e || m || n. If AB = 6, AC= 14, and EF = 8, then find EG.

A. 2(

b H "

(OK-

X =

) ®

f X

ud 1*%

1*1 C, 16 D. 20.

pagel

5. In the figure, NQ is parallel to OP and NQ = 4,_OP = 6, and MO = 8. if NO = 2, how long is OP?

A. 2 (EL) 4

C. 6 D. 10

U

IP

6. If BE || CD, find the perimeter of AACD.

A. 24 (B) 40

C. 46 D. 20

x - 9 " *-«

7. A/^eC ~ A DEC. What is the value of x?

A.

C.

19

3^

45

15

B. 30

© 3|

3 ' K

X-5.-75

Which of the following sets of points are collinear?

A. A, X, D

B?) D, X, C

C. A, Y, B

D. A, Y, E

D

4 /

xf \ 12

•i

c

^

9. The shaded region represents—

Aj part of a plane

B. a line segment

C. an angle

D. a triangle . • :

1 ;

. •

page 2 CC Geometry Midterm Review QuestSons

10. In the figure, TU |j OR Which proportion is not true?

A.

©

. QR RS

\ RU ' QR~

V

TU US

US TU

u

ST.

J .

QR TU OS TS

ST SO TU OR

11. Three non-col!inear points must be part of the same ^ ^ _ _ _ _ .

A. circle

C. line

BJ plane

D. angle

12. Find the length

A) 17 B.

C. 20 D.

9-96 - c? iG-c

of side

19

21

X.

. _ .

' \ / v 12

1 7 ^

X A radar tracking station locates a fishing trawler at a distance of 6.7km and a passenger ferry at a distance of 8.3 km. At the station, the angle between the two boats is 97°. How far apart are the two ships?

A. 10.0 km

11.3 km -

B. 11.0 km

D. 127.3 km

a9 = )a^33M2o^ 3.-1X^-7/ {r.3 ^ i l . ^ ^ 0 ^

14. In AA8C, 4C= 10, eC = 8, mZS = 90o and mzeDA = 90°. How long is CD?

A. 3.6

B. 4

C. 5

/S!) 6.4

x = %

15. What is the length of side EC to one decimal place?

A. 6.7 B. 7.4

E) 9.0 D, 14.9

42^ (7

pages CC Geometry Midterm Review Questions

16. What is the length of side CB to one decimal place?

A ; 7.5

B. 8,0

C. 10.1

D. 12.3

l(m 52> ~- 1 2 .

^ 17. Find the area of the triangle.

Xr„ 1 . ^ 5 5

thotce.6 ,= 36

30 bo 'iO

3 -hfb {p n

18. In ANPO, calculate LN to the nearest degree.

3.6 cm A-

C,

23° B.

65° D.

1 .5

3.9

25°

67°

1.5 cm 3.9 cm

19. In ARST, calculate AR to the nearest degree,

AJ 16° B. 17°

C. 26° D. 74°

2 <.;III

CD cm 2.1 cm

20. In the triangle shown, determine ZA to the nearest degree.

A. 36° ^B, 43c

C. 47° D. 54c

8 m

21. A ladder is leaning against a tree. If the angle that the ladder makes with the ground is 60°, and the ladder is 10 feet long, how far is the base of the ladder from the tree?

AJ 5 ft B. 15 ft

C. 20 ft D. 25 ft

y\ l 0

6

page 4 CC Geometry Midterm Review Questions

22. A 6\/2 meter long wire is attached to the top of a telephone pole 6 meters tall. What is the exact measure of the angle the wire makes with the ground?

A. 25° B. 30c

/ C ^ 4 5 0 D. 90c

^ 4

23,

^

:'0«*w*^w^«>t<W,^rt(lftA-«"A«,

K^iT

One end oi a ramp is raised to the back of a truck 1 meter above the ground. If the length of the ramp is 2 meters, what is the measure of the angle the ramp makes with the ground?

i t e r s t o t e — • L ines - —

A. 25° (B1 30° C. 45° D. 90c

24. Find, to the nearest integer, the number of feet in the heigh! of a building that casts a shadow 32 feet long when the angle of elevation of the sun is 64°.

A3 66 B. 67 C. 65 D. 64

25. Find, to the nearest integer, the number of feet in the length of a shadow cast on level ground by a 15-foot vertical pole when the angle of elevation of the sun is 53°.

5, 10 D. 12

26.

K

A person sights an airplane at an elevation of 50°, The airplane is flying 3000 m above the the person. What is the distance from the person to the airplane to the nearest meter?

A. 1928 m

C.> 2517 m

B. 2298 m

D. 4667 m

39

X

27. From the top of a tower 200 feet high, the angle of depression of a point A on the ground, in the same horizontal plane as the base of the tower, is 48°. Find to the nearest foot the distance of A from the base of the tower.

%&

( A J ISO B. 220 C. 160 D. 140

\tf. To the nearest whole number, how long is the missing side of the triangle?

AJ 23 B. 26

C- 34 D. 42

20 cm

16 cm

o)t6^7?

pageS CC Geometry Midterm Review Questions

X To the nearest whole number, how long is the missino Strifl nf the triannte? missing side of the triangle?

k ) 19 B. 39

C. 43 D. 44

28cii

3D* To the nearest tenth of a centimeter, what is the length of side A8?

A. 15.9 IB.] 22.6

C. 28.5 D. 35.6

X In triangle AEC, 6 = 8, c = 6 and cosA = g . Find a.

0 B. 6

a D. 9

3 2 7

- ^ 0 ^

3(^p^

c*

) / . n 7 \ Fi

triangle AEC, a = 959, b = 631 and C = 68°. Find A to the nearest degree.

C. 65° D, 71' A J 73° B. 62

pages

In AA8C, A = 30°, C = 105° and 6 = 6. Find a.

. ;3\/2 B. 6\/2 C. \/2 D. 2\/2 fl

a u?

34. In right triangle A FOR PR = 45, mzQ = 90° and mAP_= 38°. What are the measures of PQ and OR to 1 decimal place?

35. In right triangle APQR, PO = 15, mZQ = 90° and OP = 8. What is the measure of z f? to the nearest degree?

% d

S

X

(I)

To 1 decimal place, what is the length of 6C?

SNA^O

x^ ^^idKpoH CC Geometry Midterm Review Questions

37. In AA8C, AC= 10, 60 = 8, mze = 90o and mzBDA = 90°. How long is SD?

ftb-'^

X In AA8C it is given that Ae= 19, mZB= 110°, and that mZC_= 20°. J o 1 decimal place, how long are AC and BC ?

13.

y fiC'~$d.d,&C=Ulc 39. Construct the altitude of ALMW from M to LN.

40. Construct the median to side AC in AABC.

41. Construct the bisector of ZC in CJABCD.

p a g - :•• CC Geometry Midterm Review Questions

42. Construct a line through point P perpendicular to line 2.

43, Bisect ZASC using a compass and straightedge.

44. In AABC, AC= 10. BC = 8, m_ze = 90o and mLBDA - 90°. How lona is AD?

/I03.M

K=3.h

45. Construct_eciuilateral triangle ABC using tine segms^AS asjme side.

46. In A CAT, Z CAT s Z SCI and Z ATC s Z CIS. Given AS = 30 and ST = 6, find the value of x.

c

^ t f rT ^ A ^ C T

(LT S t AT CT

X [p

A

X s - o

/ ^ - {aiip

[ K^hib page B CC Geometry Midterm Review Questions

47. In AASC, AC = 10, eC = 8,_mZB=90oand mzBDA = 90°. How long is CD?

A D

/ o x

X

^ ( p ^

^ . ^

th'^M

48. Construct the altitude of AABC.

51.

The sides of a triangle are 5.46, 6.87 and 7.65. Find the smallest angle of the triangle to the nearest degree.

The three sides of a triangle are 35.0, 22.0 and 45.0. Find to the nearest degree the largest angle of the triangle.

An observer in a helicopter flying at 1000 m observes a boat at an angle of depression of 28°. To 1 decimal place, what is the horizontal distance between the helicopter and the boat?

I )oo X ' i • i .

y^ fa /?^

HoTT o

page 9 CC Geometry Midterm Review Questions

Name: Date: Geometry

Nid-Year Evaluation Review #1 What is the slope whose equation is

•) 1 ?' 1 3 ) - |

. - |

0fE

5x i line perpendicular to the line + 3 j = 8?

3 t r -6x ^

3 3

5- If a line segment has endpoints A(3x + 5,3y) and

B{x- 1,-y), what are the coordinates of the

midpoint ofAff? / 3* *

1) (x + 3,2y) % (2x + 2,y) 3) (2x + 3,>-) 4) (4x + 4,2>0

9

^ Mx *• ^

^ 3 " J

f ax t ^ ^

9

^ a 7

( y )

M is the midpoint of AB. If the coordinates of A are (-1,5) and the coordinates of A/are (3,3), what are the coordinates of 5? / ^ " ' r 5 —

1) (1,4) (-1,5^ iW) , . ( - 7 , i) 2) (2,8) >

® (7,1) ^ - M 6 4) (-5,7)

^ , The coordinates of point R are (-3,2) and the coordinates of point Tare (4,1). What is the length

of #77

1)

2)

3)

4)

2-^2

5-72 4^3

-710 d - {so

%C3 ttp10

X What is the negation of the statement "Squares are parallelograms"? 1) Parallelograms are squares. 2) Parallelograms are not squares.

It is not the case that squares are parallelograms.

4) It is not the case that parallelograms are squares.

(j. In i\ABC, D is a point on AC such that BD is a median. Which statement must be true? 1) AABD=ACBD 2) ZABDj=ZCBD

$ AD=Cp

4) BDLAC

X Which statement is expressed as a biconditional? 1) Two angles are congruent if they have the

same measure. 2) If two angles are both right angles, then

they are congruent. D Two angles are congruent if and only if

they have the same measure. 4) If two angles are congruent, then they are

both right angles.

S^ Which statement is logically equivalent to "If a triangle is an isosceles triangle, then it has two congruent sides"? 1) If a triangle does not have two congruent sides,

then it is an isosceles triangle. |2) If a triangle does not have two congruent sides,

then it is not an isosceles triangle. 3) If a triangle is not an isosceles triangle, then it

has two congruent sides. 4) If a triangle is an isosceles triangle, then it does

not have two congruent sides.

% / /

y. In the accompanying diagram of triangles BAT and

FLU, ZB = ZFandBA = FL.

Which statement is needed to prove

ABAT= AFZU?

Q5 ^ = ^ 2) AT^LU 3) ZA ^/JU 4) BA || FL

10. In the diagram of trapezoid ABCD below, diagonals AC and BD intersect at E and AABC= ADCB.

C 8

Which statement is true based on the given information? 1) ^ C = 5C 3) ZCDEsZBAD 2) CDs AD ffh ZCDB=ZBAC

/ / . In A ABC, mZA =• x, mZB = 2x ^ 2, and rnZC = 3JC + 4. What is the value of JC?

2) 31 4) 61

/S. In the diagram of A ^ 5 C below, AB = AC. The measure ofZB is 40°.

JOQ

WhaX is the measure of ZA? 1) 40° 2) 50° 3) 70°

100c

/V /a

lo. If the lengths of two sides of a triangle are 4 and 10, what could be the length of the third side? 1) 6

@ 8 3) 14 4) 16 ^ b

10 • H

14

10

rUS The pentagon in the diagram below is formed by ^ five rays.

X4 VOf (PO* Wi/hZ ^2(pp

XJ 959 = 300

X-

What is the degree measure of angle x? 1) 72 2) 96 |> 108 4) 112

The sum of the measures of the interior angles of an octagon is

^ 1800 (Z'9)I?V ((p)fW

180° 2) 360° 3) 540° % l,080c

16W

lb • The measures of two consecutive angles of a parallelogram are in the ratio 5:4. What is the measure of an obtuse angle of the parallelogram? 1) 20° -'fr~ 2) 80° 5 x ^ / y ^]W

© 1000 qv n^o 4) 160°

x - a o

loo $0

% 6

17. If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral could be a 1) rectangle 2) rhombus 3) square

trapezoid

Id. In the diagram below of APRT, Qisa point on PR,

Sis a. point on TR, QS is drawn, and z # p r = ZRSQ.

Which reason justifies the conclusion that APRT~ASRg> ID AA 2) ASA 3) SAS 4) SSS

/ £ The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is x + 7, and the base is 2x.

What is the length of the base? 1) 5 © 10 3) 12 4) 24

-.

x ^

2x y ^

i •

^(Xf739~-- 3 a

• y 9 + ^ / y f ^ < /(pq

3x9f^x-/ao -o

^ • f 7x-^o)--o 3fx+ia)rx.5)^o

v^a f y zS

hojtH

ctO. Given: AABC and AEDC, C is the midpoint of BD and_AE _ Prove: AB || DE ^jrOj-tm ml

') C is thz m/dp-f oP

M cuio/ fiG

E 3)^/ and 42 are •

rtoon dgH/tn

s) 0- rviidpi divicU^ *~ Segm&i/ info $ ~p<vh.

y) \Zej/Hc6j angles aye -

6) CPC rc

Ql, In the accompanying diagram, WA || CH and ^7 /

and AC intersect at point T. Prove that (FF7XC7) = (//7)(^7).

S^oufoTiaaf

4$ and AC art

(

bXiprXcr) : Vw

0 ga/csj

v) II h/ut coM hij &

hcwsvtrscJ form

2>) aJltsncUe /w^e//^/ OJIJUS, art ^

4) m ~ m s) (iowt&Pbrtd(ACj s/c Or Sf/fyldi JrietrtoO^

^J't' f nt^wT' -''-' ^

I PfOd^Cf of / ^ e^-kmeS Poqz \£

Name: Date:

Mifl-¥ear Evaluallon Review #2 •vT What is the negarion of the statement -Squares are

\ paralielograms"? 1) Parallelograms are squares. 2) Parallelograms are not squares.

(S) It is not the case that squares are parallelograms.

4) It is not the case that parallelograms are squares.

A Which statement is logically equivalent to "If a triangle is an isosceles triangle, then it has two congruent sides"? 1) If a triangle does not have two congruent sides,

then it is an isosceles triangle. (3% If a triangle does not have two congruent sides.

then it is not an isosceles triangle. 3) If a triangle is nor an isosceles triangle, then it

has nvo congruent sides. 4) If a mangle is an isosceles triangle, then it does

not have two congruent sides.

5)

^

Which set of numbers could be the lengths of the sides of aright triangle?

Q ) {10,24,26}

2) {12,16,30} 3) {3,4,6} 4) {4,7,8}

Given the true statements: "t is a multiple of 3" and "t is even," What could be a value of f? 1) 8

3) 15 Q 24

% The statement "Maya plays on the basketball team or Maya joins the ski club" is false. Which statement is true? /) Maya plays on the basketball ream and Maya

joins the ski club. 2) Maya plays on the basketball team and Maya

does not join the ski club. 3) Maya does not play on the basketball team and

Maya joins the ski club. ^} Maya does not play on the basketball team and

Maya does not join the ski club.

% " V

Which statement is an example of a biconditional statement? 1) If Craig has money, he buys a car.

( ^ Craig buys a car if and only if he has money. 3) Craig has money or he buys a car. 4) Craig has money and he buys a car.

V \ la the accoaiMimn? diasram. UK bisects IL and 0 ) ZHsZK.

' ) What is tiie length ofBDl

2) ^20 Q) ~J50

4) -N/IIO

' )

x ^ y H

What is title most direct method of proof that could be used to prove AHU= AKUl 1) H L s H L 2) SAS 5 SAS

(3) A A S s A A S 4) ASA = ASA

Which condition does not prove that two niaugles are congnient? 1) SSS = SSS

(2) SSA = SSA 3) SAS = SAS 4) ASA = ASA

kyi ^

) Csar^Kete the partial proof below for fee acccjncaaidag diagram by providiiig leasocs fbr steps 3,6, S, and 9.

V fad—

TKJ s.

D

A3~nE_ _

Statements

i A&OD 2 AEL3C. Dm FF SZBm&ZE&s ridit angles.

4Z3~ZE

53C{\FE S./RCA^/mD

l.iB^DE sAJBCs&Jom

9ACsFD

Reasons 1 Given

KSxm

pofrrt ri^M ^S

4 AH rigfec anstes are coaHraeat, 5Gi^-5ii

5 II llruz.5 Po^n = cdh .04-. 4 i

> GiveE.

s/)Pls=A/is

9 CPCT£.

"J Grven; P ICE is a rhombus, SEO, PEV, ZSPR s AVOR

/ / Si' --i

Prove; SE = EV

5faj-cmtn+ R eflLioyl

1)91^0^ is fi. rhombs 1 0 g i v m

a) ?e 5 ED 8)tn a rhombus, all sicUs

3) 4l - 2 9 3) I n ft ihombu.^ oppos'^

4) 4SP(l = tyot K ) gi^e^)

9) *S£P s ^ ^ o p ) ASA ^ASfl 10) S^ ^ tv/ 1 • ^ CPCtC

faf n

') jZ) In tbs diagramofAJtBC and &DEFhelaw,

.43 = DE, ZA = ZD. and ZB s ZE,

A A

f\ >

Q

5 )

/ 7 \ la the accompan^iiig diagnun, CALAB, EDIDF^

' ' EDl\J3,CBsBF.,AB = ED,aad

mZCAB = raAFDE = 90.

Whidi metiiod can be used to prove KABC^&DEFI 1) SSS 2) SAS

0 ASA 4) HL

Which statement would not be used to prove A-^SCs ADEF?

0 SSS = SSS 2) SAS = SAS 3) AAS s AAS 'V) H L s H L

'K Ink 'xsa equilateral triangle, what is the difference between the sum of the exterior angles and the sran of the interior angles?

0 > ISO'

2) 120°

3) 90=

4) 60=

Sano, = 36?^

sitm^ - ifC

15) ^ _ 5 ™ ^ _ ^

1) 41

2) 45.;

/tsx + l fv

/so?

A**w 3) 56

(3's3

\ x

41 N, ^' X ' \

^X+I^P - I^O

^K = |(p4

X - Mf

f A j If the m e a s u r e s o f the ang le s o f a t r iangle a re represen ted b y 2x. 3x - 15. and 7x + 1 5 . tlie t r iangle is

ftp an isosceles t r i ans le 3) an acute t r ianale . o y , ^ ^ ^

3X-I5 -Bo -))L*\6 ^ \QO

2) a right t r iangle 4) a n equiaagii lar t r iangle

% /r

1) In the diagram of AABC below, A3 = AC. The measure of Z 5 is 40°.

ICCP

What is the measure of Zi7 1) 40° 2) 50c

3) 70° (3) 100°

i] V.laicli stats-meat is rac* always was aboirt a

daralleicsiHa? / Ths fegBuals are coogruair,

2) The opposite sides are coagpa&A. 3) The opposite an-g!es are conspsaat. 4} The ctgposite sides are psaliel

) In the diagram below, AA3C is shown with AC extended through point D.

•"^• iKs.

Jfm/BCD = 6x- + 2, mZBAC = 3x + 15, and mZABC= 2x -1. -uiat is the \-aiue of a"?

to 5 ^ + H ~ 0>Y * 9 2) 14

3) 16 11

)Q - x 4) 18-

^ ) ) In the accompanying diagram of AABC, AB is extended to D, exterior angle CBD measures 145°, and m i C = 75.

What is mZCAS? 1) 35

© 70 3) 110 4) 220

11 )

WbeA is fee slcpe of a 1 : to die line Tiffhsjas eqisaticn is 2r = - & -r 8? 1) -3 S- "5 £)

"" 3

2)

(5 i 4) -6

nn

^ 2 ] In the accompanying diagram, AB | CD. From

point E on .-15. traasYersals Z F and EG are drawn

intersecting CD at i f and/, respectivety.

JfmZCHF= 20 and mZDIG = 60, Mhat is mZHET? 1) 60 2) 80

( ^ p 100 i ^ ^ 4) 120

fafM

ii) In the diagram below of A HOP, side HP is extended through P to J, mZQFT= 6x - 20, niZHgP = x+40r,a3idmZPH'Cl = 4T-5. Fmd mZQFT.

{x + 4or

J"/) hi APQR. PO = S, Oi? = 12, aud RP = 13. Wnich stateiEeat about the asgies ofAPOR nm.it be tnje?

(T)) mZO>mZP>imci? Q 2) mZg>mZi?>mZ? ^ / N j Q 3) mZR>mAP>mZO 4) mZP>mZS>mZ.g

cfthemeasmes of the mterior angles of BE is

1) ISO1

2) i&F 3> 540= ^ ^ )%X>

^ - c 9 ) \ < S t P

1.080c

I C P V D

(Not drawn to scale)

v - !<• I •

^

y - i ^

Mehssa is •walksng arctiEd the oKfaide cf a bialding that is in the shape of a regular poh/gon. She deteanines- thai the measure of one estedor aagLe of the buildtiia is 60^. Hoisr manv sides does the feuildins faase?

®6 ^ 3 'I^£-6D" 2) 9 4) 12 n

SI s la fee accois jssnyiiig diagram cf paralMoaram ABCD, mZ3 = 3K. and mZC=23:4-11 Find the auadser of degrees in AD-

M

X = o > M /

Given; „SXifis apaialkloaram.

Pnyve: JFiXMis a rhoaims.

S ^ c ) ^ I J T . . • . , „ • .

/

^ 0"7 \ A «padriIaSeral -ssiiose diagonals bisect each other

_' and are pespendicular is a .Qj) jbooiias

3) trapescdd 4) parallelogiam

H

n] In a certam qua^ilateral two oppxmxz sides are parallel, and fee other two opposite sides sre not congroeat This quadrilateral, could be a t) ihombus .) parallelogram

3) square ^4) trapezoid

( t c ^ o o

0 a 1 Yen

k&te>

J 1 In the diagram below of A~ACD. E is a pomt cn - iDaad5is apcimcn^C-sadiihstZSliX?, If JE= 3,ED = 6T ssdDC= 15, fed the length of E3.

&

--^7

)

) Etb^S j

Write an eqeslioa of the line thai passes tbrosah the point (6,-5) and is pandlel to the line whose equation is 2x - 3 v = 1 i

cPx-3y^ H - 3 * - 5 *

3$)

-3M = -2* + II

C ) 4 5 - | y 4

3

3 - iS - J S

Aahsnti is BEreeyitffi for a new parking let diaped liis a parallelogram. She knows that three of the vatice-i of p3i-aUdop-am.45CD are J(0,0). B(3,2), and CX6.5). Find the cocrdtEates of p>3ml D and sketch pfflraiielogi-am-i3CD cn the acccmpanying set of axes. Justify mathematkalh- that the figiae JOB have dtmsu is a parallelcgianL

i !•

( L i

1 |

(

T"" i ;; .

4f r ; '"I P i

l - ' ? .' ' i ^

; i i i

.4 i .

„

^

f 1 | j I

" - • • • • " • - " • "

& ^ 1 , • 1 <

/T/i ^ i

HU

L

j

1 r i

1 1 1

i

| 1

f

^ i I i

-

s i

"";•"; i

i

j

a

MM Mki lM,

j 1 i

™

„.

--|- ^

•fH-

„

•

"1 i

„„i

H s

i

Xxfi.B')

AT2> £ •

rn - 5

Qiadiiiateral .-IBCD has vertices -i<2,3)T Bil\ 10), 0(9,4), and 13(4,-3), Pmse that JBCD is a paraMelo|jam but not a rhombus. [Ihe Bse of the asid is cptionaL]

"Y~j

rjor)'' S h o w c p p o S i t f spies a r c = > bv A oJl 5 1 ^ 5

L o ^ d ^ i ^ : S ' ^ c ^ , o ^ p ^ ^ , ^ S\cUj^ CUe &J

Name Date

X

Mid-Year Evaluation Review #3 Given: Two is an even number or three is an even number. Determine the truth value of this disjunction. Justify your answer.

Tv f Trim,

x What is the negation of the statement "\ am not going to eat ice cream"? a. I like ice cream.

(&> I am going to eat ice cream. c. If I eat ice cream, then I like ice cream. d. If I don't like ice cream, then I don't eat ice cream.

3. The diagonal AC is drawn in parallelogram ABCD. Which method can not be used to prove that A/\fiC = ACD/\? ^ ^

a. SSS c. SAS ^ ^ — ^ ® SSA d. ASA V v t ^ ^

1> C'

4. In AABC, point D is AB, and point E is on BC such that DE \ \ AC. If DB = 2, DA = 7,

and DE = 3, what is the length of /4C?

a. 8 c. 10.5 p ^ A _£. - J l b- 9 (3)13.5 V-^AV ^ ^ ^

5. In AABC, AB = 7, BC = 8, and AC = 9. Which list has the angles of A/\5C in order from smallest to largest? Q>

a. ZA, ZB, ZC c. ZC, ZB, ZA - /"" b. ZB, ZA, ZC (d) ZC, ZA, ZB

6. In isosceles triangle ABC, AB = BC. Which statement will always be true? a. mZB = mZA (c^) mZA = rnZC g, b. mZA > mZB d. rnZC < mZB

fliqttiQ

7. Vertex A of isosceles triangle ABC measures 20° more than three times mZB. Find rnZC.

5 * + S O - I S O S ^ C ^ / ^ O r —

8. In the accompanying diagram, ABCD is a straight line, and angle E in triangle BEC is a right angle.

(X -I- d + 9 0 - S ^ o

o. + d - 9"70

A N a

q o

E

B

b^ v

n ^ \ c d^D

What does a0 + d0 equal? a. 135° b. 160 0

c. 180° 0270°

9. Given: Quadrilateral ABCD, diagonal AFEC, AE = FC, BF1AC, DELAC, Z 1 s Z 2 Prove: ABCD is a parallelogram

B C

hgirvt 0Lhgljt6

i)A\ S ^ 9

^ SUb+Y^Ol'/o^

LB) X ^ A ^ S ^^^n f^h4 angles

^^A15>f ^Acn>E 1 ^ A ^ S S'jqAS

-p curallci o q rcuno-

»^ C P C T C

^ CPCTC

opP. S i c ^ S H - * 'S i s ^ OAyoul l iL i r t r . /^ >^c/) 3

10. In the diagram below of parallelogram STUV, SV = x + 3, VU = 2x - 1, and

TU = 4x -3. What is the length of 5U? v

^ x/x-3 ^ x ^ K - 3 u - v - X -x

a ) 5 b. 2

3X-3 ^ 3

c. d.

3 X •3

7 4

= 3 ^3

3

5V- 9+3 = 5

X . What is the measure, in degrees, of each exterior angle of a regular hexagon? a. 45 c. 120 o / ,->

© 60 d. 135 ^f^ = (jQ CP

y^. The measures of five of the interior angles of a hexagon are 150°, 100°, 80°, 165°, and 150°. What is the measure of the sixth interior angle?

( j p 75° c. 105° » 6 O M O O v s-o * lk5+l6£>-«-x -I^C b. 80° d. 180° . Ile.

CCe-Q} ( ^ -190 ~ (S5 - ^ ^

X = 7 5

13. What is the slope of a line that is perpendicular to the line whose equation is 3* + 4y = 12? ^ ^ = | Q

3 4 J

a. 4

b. --

C - 7

- 3 y = x +2 -• ^

14. Write the equation of a line passing through the point (-6, 0) that is parallel to the line whose equation is 2y - 6x = -12.

3 3 * - C P | ^ 3 X - H g

PdyiM

15. What is the distance between the points A (7, 3) and B (5, -1)?

a- VlO J - Ui-5y± (ZH)*' b. VT2 c. Vl4

S)Vio d ^ \ 3 a ^ a

16. Square LMNO is shown in the diagram below.

What are the coordinates of the midpoint of diagonal /.N? y

4

- i i -*-x

a. (4.5,-2.5) b. (-3.5, 3.5)

( ' 9 ^ ^ ^ (-9.6. MS)

c. (-2.5, 3.5) ® (-2.5, 4.5)

17. The coordinates of quadrilateral JKLM are are J (1, -2), K (13, 4), L (6, 8), and M (-2, 4). Prove that JKLM is a trapezoid, but not an isosceles trapezoid.

^

c ^ ^ ^ ^

iL ^ . ^ - ^ ^

v^' s , s ^ s \ ^

£. >_ , ^ ^ - i . L ^ ^ ^ ^ %^

_. i 1^

Plan : Show basts a/e 11, 1^5 a/t no- 1 OLDOI 1^5 a/e nof ^

^of--TV =

^ 1 9 9

^MI = -iL = _Q ^ ^ = -iL

^K U ML ,

'i-K

dux ^ f l C a ^

Condusioti - SiVlcc lefls CLT^ h ^ l\ and

bases, fl^^ " ^ ^ - ^ ' ^ ^ +ira-pcs^jd,

S I A O L . -I-K^ I t ^ ^ axe npl- ^ TKLW. is ncW