SCORE 5 Test, Form 2A •Chapter - · PDF file5 Chapter 5 Test, Form 2A (coiztinued) 12. ... A 12, 9, 2 B 11, 12, 23 C 2, 3, 4 B V, \1, ‘/i 17. C 18. What is the relationship between

$Page 1: SCORE 5 Test, Form 2A •Chapter - · PDF file5 Chapter 5 Test, Form 2A (coiztinued) 12. ... A 12, 9, 2 B 11, 12, 23 C 2, 3, 4 B V, \1, ‘/i 17. C 18. What is the relationship between$
NAME DATE

__________

PERIOD

_____________

For Questions 1—4, refer to the figure.

1. Name an angle bisectoi.AKI BGL

__

2. Name a median.- -

FM GGL

__

3. Name an altitude.-

AKI BGL

__

4. Name a perpendiculisector.FM GGL

__

For Questions 5—7, refer to the figure to determine X

which is a true statement for the given information.

5. YW is an angle bisector.A LYWZ is a right angle. C X1V = WZ

B LXYW LZYW D XY = ZY

____

6. YIVis an altitude.F LYWZ is a right angle.

G ZXYW LZYW

____

7. YWisamedian.A ZYWZ is a right angle.B ZXYWZZYW

___

8. Name the longest side of Ls.ABC.FAB

GBC

_______ __

9. Name the angle with greatest measure in L.DEF.ALD CZF

B ZE B cannot tell

10. Which theorem compares the sides of the same triangle?F Hinge Theorem H Exterior Angle Inequality Theorem

G Converse of the Hinge Theorem J Triangle Inequality Theorem 10.

_____

11.Tisha wants to plant a garden in the widest corner of her triangularbackyard. The backyard is bordered by the back of the house that is 50 feetlong, fence A that is 27 feet long, and fence B that is 35 feet long. Whichcorner has the widest measure?A corner between fences A and B

B all three corners have the same meastire

C corner between the back of the house and fence A

D corner between the back of the house and fence B A

•Chapter 5 Test, Form 2A SCORE

___

Write the letter for the correct answer in the blank at the right of each question.

— DCJM DHJ 1.

__

JHJM JEt] 2.

__

ACJM DHJ 3.

__

HJM JHJ 4.

__

H XW=WZ

J xY=zY

C XW=WZ

B XY=ZY

HAG

J cannot tell

U

a,a,Ca,a£C0

z

a,

CDU

a,-CI—CCC

a,-Ca,

a,

CDU

a,CUCa,

CD

-CC)

a,’aC0

B

6. F

7.c

F

B

84’.

FI

E%

Chapter 5 51 Glencoe Geometry

NAME DATE

__________

PERIOD

_____________

5 Chapter 5 Test, Form 2A (coiztinued)

12. Find the possible values for rnLi.F 90>rnLi>74 H 0<mZl<74

G 180 > mLl> 74 J mLi = 106

13. Find the value of x.A9 C27

Bli D32

14. Which is another name for an indirect proof?F proof by deduction

G proof by converse

Prove: mLl = mLB + mLC

F Li is not an exterior angle of AABC.

G Li is an interior angle of LABC.

H mZl mLB + rnLC

J mLl=mLB

18. What is the relationship between the lengths of QSand RS?F Q$=RS H Q$>R$

G QS <RS J cannot tell

19. What is the relationship between the lengths of DCand AD?A DC<AD C DC=AD

B DC > AD D cannot tell

20. What is the relationship between the measures of Liand Z2?F mLl=rnL2

G mZl<mL2

Bonus YW bisects LKYZ in AXYZ. Point W is on XZ.IfmLXYW = 2x + 18 and mLZYW = x2— 5x,find the possible value(s) of x.

12. G

x+

x+ 7

H proof by inverse

J proof by contradiction

15. Choose the assumption you would make to start an indirect proof of x < 2.A x>2 B x2 C x=2 D x2

16. Choose the assumption you would make to start an indirect proof.Given: Li is an exterior angle of /A3C.

14. J

15. B

17. Which of the following sets of numbers can be the lengths of the sides of atriangle?A 6, 6, 12 B 6, 7, 13 C V, Vi D 2.6, 8.1, 10.2

16.H

0C

‘C

CD

C0CD

C0CD3

DC0C

0C0

CD

C,0CD5I

003CDCCD

CC,

D17.

_____

R AT

________

H

BB19.

_____

83

20. H8

B: 9,—2

C

H rnLi > rnL2

J cannot tell


NAME

________________________________________

DATE

__________

PERIOD

_____________

• 5 ‘Chapter 5 Test, Form 1 SCORE

____

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1—4, refer to the figure at the right.G

1. Name an altitude. A

ADEE F

DCF

____ __

C IB’ D

2. Name a perpendicular bisector.HFDE GAB HGB JCF 2.

__

3. Name an angle bisector.DADE BAB CGB DCF 3.

__

4. Name a median.“S -

FDE GAB HGB JCFB

For Questions 5—7, refer to the figure to determine C

which is a true statement for the given information. A D5. AC is a median.

ArnLACD=90 C BC=CDB ZBAC LDAC D LB LD 5. C

g 6. AC is an angle bisector.FmLACD=90 G LBACLDAC H BC=CD J LBLD 6. G

7. AC is an altitude.A mLACD =90 B ZBAC LDAC C BC A

8. Name the longest side of L.DEF.FDE HDF

B HG EF J cannot tell 8.

_____

5 7

9. Which angle in Chas the eatest measure? A C

ALA CLCBB P cannot tell 9.

_____

10. Which theorem compares two sides and the included angle of two triangles?F Hinge TheoremG Converse of the Hinge TheoremH Exterior Angle Inequality Theorem

FJ Triangle Inequality Theorem 10.

_____

11. Which assumption would you make to indirectly prove x> 5?BA x<5 B x5 C x=5 P x>5 11.

___


NAME

________________________________________

DATE

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PERIOD

_____________

5 ‘Chapter5Test, Form 1 (continued)

12. Find the possible values for mLi.

F 180>rnZi>62 H 0<mLl<62

G 90 > mLi > 62 J mZl = 11862

12. F

13. Find the value of x.A5 cio M\

B 7 B 15 x+3 1513. B

W/IN

14. If D is the circumcenter of /.IABC and AD = 6, find RD. BFt 119

G6 J12 14. G

A C

15. Choose the assumption you would make to start an indirect proof of x > 3.A x<3 B x3 C x3 D x=3 15. C

16. Choose the assumption you would make to start an indirect proof.Given: aProve: Li and L2 are not supplementary.F aWb H L1L2

GG Li and L2 are supplementary. J Li and L2 are complementary. 16.

_____

17. Which of the following sets of numbers can be the lengths of the sides of atriangle?A 12, 9, 4 B 1, 2, 3 C 5, 5, 10 D \/, V, v’i 17. A

B18. BF is a median of LBEC. If EC = 15. find FC.

F5 1110G

G 7.5 J 30 AD E F

C 18.

_____

For Questions 19 and 20, refer to the figures. A19. Given: AC DF, AB DE, ,nLA > rnLD

Which can be concluded by the Hinge Theorem? B “C

A L\ABC ADEF C BC <EF D

B BC=EF D BC>EFE/”\

19. D

20. Given: AB DE, BC EF, AC <DFWhich can be concluded by the Converse of the Hinge Theorem?F mLB <rnLE H mLB = mLE

G mLB > mLE J ABAC LEDF 20. F

Bonus QS is a median of APQR with point $ on FR.

If PS = x2 — 3x and SR = 2x + 6, find the possible6 1

value(s) of x. B:

____________


NAME DATE

__________

PERIOD

_____________

r..s2ai;tJii:est, Form 2B SCORE

___

Write the letter for the correct answer in the blank at the right of eachquestion.

For Questions 1—4, refer to the figure.1. Name a median.

ARW

BSV

__

2. Name an angle bisector.FRW GV HQT

3. Name a perpendicular bisector.ARW

___

4. Name an altitude.FRW GRF

__

For Questions 5—7, refer to the figure to determine Dwhich is a true statement for the given information. G

5. FG is an altitude.A ZDGF is a right angle. C DG = GEB DF = EF B ZDFG IEFG

___

6. FG is a median.F LDGF is a right angle.

G DF=Ef

___

7. FG is an angle bisector.A ZDGF is a right angle.B DF=EF

___

8. Name the longest side of AABC.FAB

GBC

__

9. Name the angle with the greatest measure in t.GHI.ACG CLI H

B LH B cannot tell

____

10. Two sides of a triangle are congruent to two sides of another triangle and theincluded angle in the first triangle has a greater measure than the includedangle in the second triangle. These are the assumptions of which theorem?F Hinge Theorem H Exterior Angle Inequality TheoremG Converse of the Hinge Theorem J Triangle Inequality Theorem

_____

CQTDRU

BSV

-

JRU

CQT

HQT

—

DRU

-

JRU

1. -

2.

____

F

5A

6.H

9.c

10. F

aC

C

00

0a

C

I-.0C0C>

•0C,

z

C,

(!Ja

C0aCC

0

C,

>‘000

H DG=GE

J LDFG LEFG

C DG=GE

D LDFG LEFG

H AC

J cannot tell

B

62

A7O 48


NAME

______________________________________

DATE

__________

PERIOD

____________

5 ‘Chapter 5 lest, Form 2B

11. Carrie, Maria, and Nayla are friends that Naylalive close to one another. Which two friendshave the shortest distance between them?

(20x + 7)A Maria and Nayla

B Carrie and Maria

C Carrie and NaylaCarrie

(5x + 50) (5x +Maria

D All three live equal distances fromeach other. 11.

______

12. Find the possible values for mLi.F mLi=i24 H90>mLl>56

56 1G 0 <mLl <56 J 180 > rnLl > 56 12.

____

R—13. Find ST. $

A 12 C 23‘° 2x—1

B 18 D 24 x+6 TI14. Which of the following is the last step in an indirect proof?

F show the assumption true H show the conclusion false

G show the assumption false J contradict the conclusion 14. G

15. Choose the assumption you would make to start an indirect proof of x 1.Ax>1 Bx=1 Cx<1 Dx1

16. Choose the assumption you would make to start this indirect proof.Given: AB bisects LCAD.Prove: ZACB LDABF AB does not bisect LCAD. H AB is a median.

G AACD is isosceles. J ZACB LDAB 16.

____

17. Which of the following sets of numbers can be the lengthsof the sides of a triangle?A 12, 9, 2 B 11, 12, 23 C 2, 3, 4 B V, \1, ‘/i 17. C

18. What is the relationship between the lengths of YW and YX?F YW=YX H YW>YX Z

G YW < YX J cannot tell x w 18. G

19. What is the relationship between the lengths of DG and GF? 0

A DG>GF C DG=GF E&NB DG < GF B cannot tell 19. A

20. What is the relationship between the measures of Li and L2? F

F rnLl = mL2 H mZl > mL2 N 10 K

G rnLl <mL2 J cannot tell 20. H

Bonus HJ is an altitude of AGHI with point J on M

IfmLGJH=5x+30,GH=3x+4,HI=5x—3,160JI = 4x — 3, and GJ = x + 6, find the perimeter of AGHI. B:

___________


NAME DATE

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PERIOD

____________

I Chapter 5 lest, Form 2C SCORE

______

2. The perimeter of AR CD is 44. Findthe value of x. Then describe therelationship between and BD.

3. If point E is the centroid of AABC, B

BD = 12,EF = 7, andAG = 15, find ED.

AC

4. The vertices of LXYZ are X(—2, 6), Y(4, 10), and Z(14, 6). findthe coordinates of the centroid of LIXYZ. 4.

5. If O is an angle bisector of ZMON,find the value of x.

6. A biker will jump over a ramp,where x and z are measured infeet. Write an inequality relatingx and z.

7. List the angles of LGHI in order fromsmallest to largest measure.

8. List the sides of APQR in order fromshortest to longest.

9. Find the shortest segment.

11. Write the assumption you would make to start an indirectproof of the statement. If AR is an altitude of equilateraltriangle ABC, then AR is a median. 11.

AB is not amedian.

1. Name an angle bisector. 1.

D

B

x = 8; AC is thei..

2. bisector of BD.

3. 4

16 223’ 3

25((X+155.

P

(z+3)7Q.

6.

0C

‘aa,C‘a

2a,0

C,

00

a,-CF

0C0

a,-a,a,

‘a

00

a,00Ca,

0

a,’

000

2(z + 3) >

21n.ci, cH, cG

45\PQ, PR, QR

XC9.

w10. Write the assumption you would make to start an indirect

proof of the statement. If 16 is a factor of n, then 4 is a factorof n. 10. 4 is not a factor of n.


NAME DATE

__________

PERIOD

____________

“:: 5 Test, Form 2C (continued)

12. Write the assumption you would make to start an indirectproof for the following.

Given:XY YZYWbisects ZXYZ.

Prove: LX LZ

13. The measures of two sides of a triangle are 10 meters and23 meters. If the measure of the third side is x meters, findthe range for the value of x. 13.

14. U is a median of APTQ. //‘cIf UQ = 6, find TQ. / / ft \ N

15. If bisects C, find the value of x.

B

16. Write an inequality to compare EF H 6 Eand GH. 2O

17. Write an inequality to compare mZland mL2.

For Questions 18—20, complete the proof below bysupplying the missing information for each correspondinglocation.

Given:AD = CB andAC > DBProve: mLADC > mLDCB

_______

Bonus Write an equation in slope-interceptform for the altitude to BC.

12. LXLZ

13m<x<33m

12

34

EF<GH

12 It

ft5 ft

mLl > mL2

14.

15.

16.

17.

Definition of

18. segments

Proof:Statements

AB

Reasons

1.AD=CBandAC>DB

2. ADCB

3. CDCD

4. mZADC > mLDCB

0C

S00m

00

a

U,CS0

CD

00CD

I

00

CDS(0‘C

S0

1. Given

2. (Question 18)

3. (Question 19) 19. Reflexive Prop.

(Question 20) 20. Converse of Hinge Th.

B(2a. 2b)

B:

= c—a

01,4(0 0) C(2c, 0)

Chapter 5 56 Glencoc Geometry

NAME DATE

__________

PERIOD

____________

5 ffChapter5Test, Form 2D SCORE

______

2. The perimeter ofFRQS is 34. Find the valueof x. Then describe the relationship between

and FQ.

3. If point N is the centroid of ZHIJ,IM = 18, KW = 4, and HL = 15, find JN.

6. A rubber doorstop has aside measuring 7z anda height measuring x — 5. Writean inequality relating x and z.

7. List the angles of ATUV in orderfrom smallest to largest measure.

8. List the sides of LSFGH in orderfrom shortest to longest.

9. Name the longest segment.

8

19 32’ 2

20

F —

/N 8. FH,GH,GF

HI’82 41”\G

L 30 70 M

K”

11. Write the assumption you would make to start an indirectproof of the statement. If AD is an angle bisector of equilateraltriangle ADO, then AD is an altitude. 11.

Ab is not analtitude.

1. Name a perpendicular bisector. G 1.

x=5; RSisthe..Lbisector of PQ.

R10 4x—10 2.

Q)

2x—3 S

3.H -a

4. The vertices of L,.DEF are D(4, 12), E(14, 6), and F(—6, 2).Find the coordinates of the circumcenter of LDEF.

T (5x—10)’

5. If RU is an altitude for /RST, find Rthe valuex. U

S

4.

l5O

5.

6.

CC

a,C‘aaS00

S‘a0C

a,-cF.

0C0‘a>•0‘a

I

S‘a

0C

a’0CCa,

0

.00,

a,‘a.00

7z > x —5

.8

5 7. LT,LV,LU

9.

10. Write the assumption you would make to start an indirectproof of the statement. If n is an even number, then n2 is aneven number.

,.2 is not an even

10. number.


NAME DATE

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PERIOD

_____________

(5 Chapter 5 lest, Form 2D (continued)

12. Write the assumption you would make to start an indirectproof for the following.Given: Vis not the midpoint of PQ; <PProve: SV PQ.

_______

PQ

13. The measures of two sides of a triangle are 14 feet and 29 feet.If the measure of the third side is x feet, find the rangefor the value of x.

14. BD is a median of AABE. If AD = 8, find DE.

A

12. SV±PQ

13. 15ft<x<43ft

14. 8

A DE F C

15. If bisects /XYZ, find the value of x.3x— 20

w2x+ 15

Y

16. Write an inequality relating mz1 7and rnL2.

17. Write an inequality relating BC cand ED. B48

For Questions 18—20, complete theE

proof below by supplying the missinginformation for each corresponding location.Given: K is the midpoint of AB. M

mZMKB <mZMKAProve: MB <AM

B K AProof:Statements Reasons

15. 35

16. mU < mU2

17. BC<ED

Midpoint18. Theorem

1. K is the midpoint of AB.mZMKB < mLMK4

2. BKKA

3. MK MK

4.M3 <AM

00•0

C0

©00D00CD

0G)DCa

DC

DC0

0

0

00DCaI

00

•0DCSCDDC

S0

1. Given

2. (Question 1$)

3. (Question 19)

4. (Question 20)

Bonus Write an equation in slope-interceptform for the perpendicular bisectorof CE.

Reflexive Prop.19.

20. HingeTh.

c)

B:OC(0. 0) Eta, 0) X

x =


NAME DATE

___________

PERIOD

_____________

• 5 Chapter 5 lest, Form 3

1. If point G is the centroid of LABC, C

AR = 24, DG = 5, and CG 14, D EfindDB.A

FB

SCORE

______

U

a,a)Ca)a£00

‘a0U

a,-CI.0C0

a,

0a,

I

a,

0U

a,0UCa,

0

-C0

a,’a00

3. If JL is a median for LIJK, find thevalue of x.

IK3x+1O L 2x+42

32

1.

2. The vertices of AEFG are E(2, 4), F(1O, —6), and G(—4, —8).Find the coordinates of the orthocenter of LEFG. 2.

15

(38 32I73’ 12

146>mLL>O4.

5 LH,ZI,LG

6. QR, PQ, PR

4. Write a compound inequality for the L

possible measures of LL. M

5. List the angles of LGHI in order from G

smallest to largest measure.

6. List the sides of FQR in order from Qshortest to longest. so’

‘ R

7. Name the shortest and the lonoest X

segments. W_/\\

72y

V

8. Write the assumption you would make to begin an indirectproof of the statement. If 2x + 6 = 12, then x = 3.

9. Determine whether 8, 4, and 2 can be the lengths of the sidesof a triangle. Write yes or no. Explain.

10. Write the assumption you would make to begin an indirectproof of the statement. The three angle bisectors of a triangleare concurrent.

11. Write and solve an inequality for x.

shortest: W;longest: VW

x#3

9- no;2+4<8

The L bisectors are

in not concurrent.

112x— 31)’1 0

11

12x — 31 > 3x — 4;x>3


NAME

L5 Chapter 5 lest, Form 3 contiiued)

12. If FH is a median of LEFG find the F

perimeter of /EFG.

_____________G

2x+23H 7x—2

000

c0

6

to

C)0to

C)G)to

to0.Cto00

0

-.40•to

C)0to

I

003

•0to0toto

0C)

DATE

___________

PERIOD

_____________

12.

13. Write the assumption you would maketo start an indirect proof for the following.Given: AB DR and AC CDProve: ZB

140

B>E

14. The measures of two sides of a triangle are 24 inches and29 inches. If the measure of the third side is x inches, find therange for the value of x.

LBLE

15. YW is the perpendicular bisector of ZT.If TW = 3, YW 8, andXZ = 12. FindXY.

16. Write and solve an inequality forthe value of x.

13.

14. 5 in. < x < 53 in.

15. 17

3x + 10 > x + 20;

16. x>5

z w

8 3x+1O

x68


Given:XW=YZ,XK>WK,andKZ>KY yProve: mLXWZ > mLYZW K

Proof: z WStatements Reasons

1.XW=YZ,XK> WK,and KZ>KY

2.XW YZ

3.XZ> WY

4.WZWZ

5. mZXWZ > mZYZW

1. Given

2. (Question 17)

3. (Question 1$)

4. (Question 19)

5. (Question 20)

17. Def. of segments

Addition Prop. of1 S Inequality

Bonus Write an equation in slope-interceptform for the line containing themedian to DE.

Reflexive Prop.

20. Converse of Hinge Th.

yE(2c. 2c

— d 2ad

B:‘ c—2a c—2a

OID(O, 0) F(2a, 0)


NAME DATE

__________

PERIOD

____________

[5/Chapter 5 lest, Form 3 SCORE

____

1. If point G is the centroid of L43C, CAR = 24, DG 5, and CG = 14,

EfindDB.A

FB

2. The vertices of /EFG are Et2, 4), F(1O, —6), and G(—4, —8).Find the coordinates of the orthocenter of AEFG.

_____________________

3. If JL is a median for 7IJK, find thevalue of x.

____________________

4. Write a compound inequality for thepossible measures of ZL. M

____________________

5. List the angles of /GHI in order from G

smallest to largest measure.

_____________________

6. List the sides of PQR in order from Qshortest to longest. 8O

______________________

W\

\72y

V

8. Write the assumption you would make to begin an indirectproof of the statement. If 2x + 6 = 12, then x = 3. 8.

9. Determine whether 8, 4, and 2 can be the lengths of the sidesof a triangle. Write yes or no. Explain.

10. Write the assumption you would make to begin an indirectproof of the statement. The three angle bisectors of a triangteare concurrent.

11. Write and solve an inequality for x.

1. 15

(38 32il3’ 12

3x+1O L 2x+42

2.

32

146>mLL>O4.

5. LH,LI,LG

6. QR, PQ, PR

7. Name the shortest and the longestsegments.

UC

0,a)C

aS00

S0,

0U

-CI-.

0C00,

>

0,

I

S0,

0U

a)0UCa,0©

0,

a,’a00

7.

shortest: i7Vlongest: VW

x#3

9 no;2+4<8

The L bisectors arenot concurrent.

(3x —

(12x— 31)’11.

12x—37 >3x—4;x>3


NAME DATE

__________

PERIOD

____________

5 / Chapter 5 Test, form 3 (continued.)

12. If FH is a median of LEFG, find theperimeter of LEFG.

13. Write the assumption you would maketo start an indirect proof for the following.Given: AR DR and AC CDProve: LB LE B>E 13. LBCE

14. The measures of two sides of a triangle are 24 inches and29 inches. If the measure of the third side is x inches, find therange for the value of x. 14.

15. V is the perpendicular bisector of ZT.If TW = 3, YW 8, andXZ = 12. FindXY.

0C

CDCD

0CDCDC,CCD

C,

0CD3

CD

CDCCD

C

CD

C,

0CD3I

0C3V

CDCDCCD

CDC,

12.2x+23H 7x—2

140

5 in. < x < 53 in.

7715.--

-\ Tz

R -i-1fl 3x + 10 > x + 20;x>5

16. Write and solve an inequality for84the value of x. 16.


Given: XW = YZ, XK> WK, and KZ > KY y

Prove: mLXWZ > mLYZW K

Proof: z wStatements Reasons

1. XW = YZ, XK> WK,and KZ>XY

2.XW YZ

3.XZ> WY

4.WZWZ

5. mLXWZ> mLYZW

1. Given

2. (Question 17)

3. (Question 18)

4. (Question 19)

5. (Question 20)

17.Def. of segments

Addition Prop. of18. Inequality

Bonus Write an equation in slope-interceptform for the line containing themedian to DE.

19. Reflexive Prop.

20. Converse of Hinge Th.

E(2c.2th— d 2ad

%_%

B: C — 2a —

U) F(2a, 0)


Documents

SCORE 5 Test, Form 2A •Chapter - · PDF file5 Chapter 5 Test, Form 2A (coiztinued) 12. ... A 12, 9, 2 B 11, 12, 23 C 2, 3, 4 B V, \1, ‘/i 17. C 18. What is the relationship between