Standardized Test Practice€¦ · If mML⁀ 5 175° and mON⁀ 5 15°, ... /CKN > /KNC, /CRN >...

© C

arne

gie

Lear

ning

Chapter 9 Assessments 1401

9

Standardized Test Practice

Name Date

1. If m ⁀ WY  5 40°, m ⁀ XZ  5 30°, and m ⁀ WZ  5 60°, what is the measure of ⁀ XY ?

W

YX

Z

C

a. 5°

b. 10°

c. 15°

d. 20°

2. If m ⁀ VW  5 55° and m ⁀ YZ  5 25°, what is the measure of /VXY?

V

WZ

25°55°X Y

a. 80°

b. 100°

c. 140°

d. 160°

© C

arne

gie

Lear

ning

1402 Chapter 9 Assessments

9

3. A woodcarver draws cut lines on the top of a wooden disc. She uses the drawing of her design, as shown. In circle O, chords

___ BF   and

___ CE   are perpendicular to diameter

___ AD  . Which of the following

relationships is true?

F

E

H

C

OG

B

A

D

a. AG 5 OH

b. CH 5 HE

c. FG 5 HD

d. BG 5 HE

4. Veronica copies a map of the paths in a park with circular picnic areas. On her map, lines AC and BF are tangent to circle D at points A and E, respectively. Also, lines AC and BF are tangent to circle G at points C and F, respectively.

GFE

D

A B C

Which of the following statements is true?

a. CA 5 BF

b. BA 5 BE

c. BF 5 2BE

d. AB 5 EF

Standardized Test Practice page 2

© C

arne

gie

Lear

ning


9 5. Two secants intersect two concentric circles. The arcs include m ⁀ XZ  5 144°, m  ⁀ WY  5 90°, and m ⁀ DF  5 40°.

What is the measure of ⁀ AB ?

W

X

E

DA

F

40° 144°90°

YZ

B

a. 117°

b. 138°

c. 176°

d. 194°

6. If m  ⁀ ML  5 175° and m ⁀ ON  5 15°, what is the m/MPL?

M

ON

L

A

P

a. 80°

b. 85°

c. 90°

d. 95°


Name Date

© C

arne

gie

Lear

ning


9

7. A circular token in a board game has two triangles drawn on it, as shown. For which of the following conditions would ⁀ AB  > ⁀ BC  in circle M?

A B

CM

a. ____

MB   > ____

MC  

b. ___

AB   > ___

BC  

c. ____

CM   > ____

AM  

d. ____

MA   > ____

MB  

8. Which of the following statements about figures associated with circles is true?

a. A secant intersects a circle in three points.

b. A secant is a tangent.

c. A diameter is a chord.

d. A tangent includes a segment called a chord.

9. Secants ___

CE   and ___

BD   intersect at point A.

A

D

O

E

B

C

Which of the following is equal to AC?

a. (AB ? AD)

_________ AE

   

b. (AB ? AE)

_________ AD

   

c. (AB ? AE) ? AD

d. (AB ? AD) ? AE


© C

arne

gie

Lear

ning


910. The endpoints of diameter

___ BD   in a circle form an angle with point C. What is the measure of /BCD?

A

D

B

C

a. 180°

b. 90°

c. 60°

d. 45°

11. What statement is missing from the following proof that relates arc and angle measures for intersecting chords?

CEF

AD

B

1. Chords ___

AE   and ___

BD   intersect at point F. Given

2. Draw chord BE. Construction

3. m/AEB 5 1 __ 2 m ⁀ AB , m/DBE 5 1 __

2 m ⁀ DE  Inscribed Angle Theorem

4. --------------------------------------- Exterior Angles Theorem

5. m/DFE 5 1 __ 2 m ⁀ AB  1 1 __

2 m ⁀ DE  Substitution Property steps 3–5

6. m/DFE 5 1 __ 2 (m ⁀ AB  1 m ⁀ DE ) Distributive Property

a. m/DFE 5 m/AFB

b. m/DFE 5 m/AFD 2 m/AFB

c. m/DFE 5 m/AFB 1 m/DBE

d. m/DFE 5 m/AEB 1 m/DBE


Name Date

© C

arne

gie

Lear

ning


9


12. In circle A, chords ___

BD and ___

CE intersect at point F. The lengths in feet of each segment are shown. What is the length of

___ FE ?

AE

F

12

10 8C

B

D

a. 4.8 feet

b. 5 feet

c. 9.6 feet

d. 10 feet

13. Angle T is inscribed in two circles that share point T. Which of the following statements is true?

SQ

R

T

P

a. PQ 5 1 __ 2 QT

b. m ⁀ PR 5 m ⁀ QS

c. m ⁀ QS 5 1 __ 2

m ⁀ PR

d. m ⁀ QS 1 m ⁀ PR 5 m ⁀ QTS

© C

arne

gie

Lear

ning


9


Name Date

14. K, N, and R are points on circle C. Chords ___

RN   and ___

NK   form an angle that intercepts the same arc, ⁀ KR . Juliet defines m/KNR 5 x and m/KNR 5 y. Identify the missing reason in the proof that

1 __ 2 m ⁀ KR  5 m/KNR.

C

O K

N

R

Statement Proof

1. /KNR is inscribed in circle C, where point C is in the interior of /KNR. m/KNC 5 x and m/RNC 5 y

Given

2. Draw segments RC and KC. Construction

3. ___

CR   > ___

CK   > ___

CN   Radii of the same circle are congruent.

4. /CKN > /KNC, /CRN > /RNC Isosceles Triangle Base Angle Theorem

5. m/CKN 5 x, m/CRN 5 y Substitution Property steps 1 and 4

6. m/KCO 5 2x, m/RCO 5 2y Exterior Angle Theorem

7. m ⁀ KO  5 2x, m ⁀ RO  5 2y A central angle is equal to the measure of its arc.

8. m ⁀ KR  5 m ⁀ KO  1 m ⁀ OR  -------------------------

9. m ⁀ KR  5 2x 1 2y Substitution Property steps 7 and 8

10. 1 __ 2 m ⁀ KR  5 x 1 y Division Property of Equality

11. m/KNR 5 m/KNC 1 m/RNC Angle Addition Postulate

12. m/KNR 5 x 1 y Substitution Property steps 1 and 11

13. 1 __ 2 m ⁀ KR  5 m/KNR Substitution Property steps 10 and 12

a. Inscribed Angle Theorem

b. AA Similarity Postulate

c. Addition Property of Equality

d. Arc Addition Postulate

© C

arne

gie

Lear

ning


9


15. Fill in the missing reason from the proof of the Equidistant Chord Conjecture.

O

R

K L

S

N

M

P

Q

Given ___

KL   > ____

MN  , where radii ___

OP   and ___

OS   are perpendicular to ___

KL   and ____

MN   respectively, prove that ____

MN   and

___ KL   are equidistant from point O.

Statements Reasons

1. ___

KL   > ____

MN  , ___

OP   and ___

OS   are perpendicular to ___

KL   and

____ MN  

Given

2. Draw radii ___

OK  , ___

OL  , ____

OM  , and ____

ON  . Construction.

3. ___

OK   > ___

OL   > ____

OM   > ____

ON  . ----------------------------------

4. nOKL > nONM SSS Congruence Theorem

5. /L > /NCorresponding parts of congruent triangles are congruent

6. ⁀ OQL  and ⁀ ORN  are right angles. Definition of perpendicular lines

7. ⁀ OQL  > ⁀ ORN  All right angles are congruent.

8. ⁀ OQL  > ⁀ ORN  AAS Congruence Theorem

9. ____

OQ   > ___

OR  Corresponding parts of congruent triangles are congruent

10. OQ 5 OR Definition of congruent segments

11. ___

KL   and ____

MN   are equidistant from the center point.

Definition of equidistance

a. Radii of the same circle are congruent.

b. Definition of perpendicular segments.

c. Reflexive Property of Equality

d. Definition of segment bisector

© C

arne

gie

Lear

ning


9


Name Date

16. Secants ___

FH   and ___

GI   intersect at point J. The lengths of three secant segments in inches are shown. The length of secant segment IJ is x inches. Which of the following shows the relationship between the secant segments?

O

2

810

F

I

J

x

G

H

a. 10 ? 2 5 8 ? x

b. 8 ? 2 5 10 ? x

c. 10 ? 2 5 10 ? x

d. 10 ? 2 5 (10 1 x) ? x

© C

arne

gie

Lear

ning


9


17. Gilbert is almost finished of a proof of segment lengths for tangent ___

AB   and secant ___

AD   intersect at point A outside circle O, as shown. What line is missing from his proof?

OB

A

D

C

Statements Reasons

1. Tangent ___

AB   and secant ___

AD   intersect at point A outside circle O.

Given

2. Draw segments BC and BD. Construction

3. m/BDA 5 1 __ 2 m ⁀ BC  m/BCA 5 1 __

2 m ⁀ BC  Inscribed Angle Theorem

4. m/BDA 5 m/BCA Substitution Property step 3

5. /BDA > /BCA Definition of congruent angles

6. /BAC > /DAB Reflexive Property

7. nBAC nDAB AA Similarity Postulate

8. AB ___ AD

   5 AC ___ AB

   --------------------------------------------

9. (AB)2 5 AD ? AC Multiplication Property of Equality

a. Arc Addition Postulate

b. Vertical Angle Theorem

c. Corresponding sides of similar triangles are proportional.

d. Corresponding parts of congruent triangles are congruent.

© C

arne

gie

Lear

ning


9


Name Date

18. In circle G, inscribed angle /HIJ measures x degrees. Which of the following describes the measure of ⁀ HJ ?

G

H

J

I

a. 2x

b. x

c. 1 __ 2 x

d. 1 __ 4 x

19. Segments ___

OX   and ___

OX   are perpendicular to chords ___

AB   and ___

YZ  . If ___

OX   is congruent to ____

OC  , and the length of

___ AB   is 10 millimeters, what is the length of

___ YZ  ?

O

A

C

Y

Z

X

B

a. 8 millimeters

b. 9 millimeters

c. 10 millimeters

d. 12 millimeters

© C

arne

gie

Lear

ning


9


20. Circle O has a tangent line ____

WX   that it intersects at point X and a secant line ___

YZ  . If ____

WX   5 4 inches and ___

YZ   5 8 inches, what is the length of ____

WY  ?

O

W

Z

XY

a. 0.5 inch

b. 2 inches

c. 2.5 inches

d. 4 inches

Standardized Test Practice€¦ · If mML⁀ 5 175° and mON⁀ 5 15°, ... /CKN > /KNC, /CRN >...

Documents

Transcript of Standardized Test Practice€¦ · If mML⁀ 5 175° and mON⁀ 5 15°, ... /CKN > /KNC, /CRN >...