math iii geometry review name 1. what is ... -...

Math III Geometry Review Name _____________________________

1. What is the value of x?

93.5°

Drawing not to scale

D

E

F|

|

x º

a. 86.5°b. 43.25°c. 133.25°d. 46.75°

2. Justify the last two steps of the proof.

Given: and Prove:

R

S T

UProof:

1. 1. Given

2. 2. Given

3. 3.

4. 4.

a. Symmetric Property of ; SSSb. Reflexive Property of ; SASc. Reflexive Property of ; SSSd. Symmetric Property of ; SAS

3.What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?

A

B C D

a.b. c.d.

4. Which triangles are congruent by ASA?

T

U

V)

)

)

G

F

H

(B

C

A

(

(

(

a.b.c.d. none

5.Name the theorem or postulate that lets you immediately conclude

A

D

C

B

(

(

a. AASb. SASc. ASAd. none of these

6. From the information in the diagram, can you prove ? Explain.

a. yes, by ASAb. yes, by AAAc. yes, by SASd. no

7.Supply the missing reasons to complete the proof.

Given: and

Prove:

Q

TP

S

R

a. ASA; Substitution c. AAS; Corresp. parts of b. SAS; Corresp. parts of d. ASA; Corresp. parts of

8.What is the value of x?

38°


2121

xº

a. 71°b. 142°c. 152°d. 76°

9. Find the values of x and y.

A

DB C

||

((

47°


y°

x°

a.b.c.d.

10. Find the value of x. The diagram is not to scale.

T U(3x – 50)° (7x)°

S

R

||

a.b.c.d. none of these

11. For which situation could you immediately prove using the HL Theorem?

a. I onlyb. II onlyc. III onlyd. II and III

12. Find the value of x.

16

3x – 4

a. 4b. 8c. 6.6d. 6

13. bisects Find the value of x. The diagram is not to scale.

D

F

E

G

|

|

30°

15x

8x + 42))

a. 2342

b. 90c. 30d. 6

14. Q is equidistant from the sides of Find The diagram is not to scale.

S

Q

T

R

|

|

(8x – 11)°(4x

+ 5)°

a. 21b. 42c. 4d. 8

15. Which diagram shows a point P an equal distance from points A, B, and C?a.

b.

c.

d.

16. Find the circumcenter of the triangle.

(–3, –2)

(–3, 3)

(1, –2)

5–5 x

5

–5

y

a.

(12 , 1)

b.

( 1, 12 )

c.

(–3, 12 )

d. ( 1, –2)

17.Where is the circumcenter of any given triangle?a. the point of concurrency of the altitudes of the

triangleb. the point of concurrency of the perpendicular

bisectors of the sides of the triangle

c. the point of concurrency of the bisectors of the angles of the triangle

d. the point of concurrency of the medians of the triangle

18. Name the point of concurrency of the angle bisectors.

a. A b. B c. C d. not shown

19. In ACE, G is the centroid and BE = 9. Find BG and GE.

C

FA

D

E

BG

a.

BG = 21

4 , GE = 63

4b. c. d.

BG = 41

2 , GE = 41

2

20.Name a median for

C B

A

F

D E

|

|

))

a.b.c.d.

21. For a triangle, list the respective names of the points of concurrency of • perpendicular bisectors of the sides• bisectors of the angles• medians• lines containing the altitudesa. incenter

circumcentercentroidorthocenter

c. circumcenterincenterorthocentercentroid

b. circumcenterincentercentroidorthocenter

d. incentercircumcenterorthocentercentroid

Are the polygons similar? If they are, write a similarity statement and give the scale factor.

22.

W U

V

T R

S

Not drawn to scale.

12

18

10

1532º

32º

a.

;

c.

; b.

;

d. The triangles are not similar.

23.

21.6

9

1.8

21.6

9

1.8

4.684.68

Not drawn to scale.

A B

CD

K

L

M

N

a. ; 9 : 1.8 c. ; 9 : 4.68b. ; 21.6 : 1.8 d. The polygons are not similar.

The polygons are similar, but not necessarily drawn to scale. Find the value of x.

24.

a. x = 8b.

x = c. x = 9

d. x = 10

25.Are the two triangles similar? How do you know?

60° 60°

53°

67°

C E F H

D

G

a. yes, by SASb. yes, by SSSc. yes, by AAd. no

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

26.A

B

C

5 5

8

O M

7.5

12

N

7.5

a. ; SSSb. ; SASc. ; AA

d. The triangles are not similar.

27.a. ; SASb. ; SASc. ; SSSd. The triangles are not similar.

28. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

a. 20 ft b. 38.4 ft c. 55 ft d. 25 ft

Find the geometric mean of the pair of numbers.29. 6 and 10

a. 66b. 70c. 60d. 2 15

30. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.

7 21a. 28

b. 7 3c. 147d. 2 7

31. What is the value of x?

x

x + 5 x + 1

x – 2

>

>

a. 5b. 2.5c. 7.5d. 10

32.What is the value of x?

3x 3x + 7

5x – 84x>

>

>

a.

b.

c.d.

33. bisects , LM = 18, NO = 4, and LN = 10. What is the value of x?

L

N

M

Ox

a. 7.2b. 45c. 5.43d. 2.22

34. Find the measure of .The figure is not drawn to scale.

B

A

D50°

O

C

35°

E

27°103°

a. 130b. 230c. 140d. 120

35. The circumference of a circle is 60 cm. Find the diameter, the radius, and the length of an arc of 140°.a. 60 cm; 30 cm; 23.3 cmb. 60 cm; 120 cm; 11.7 cmc. 120 cm; 30 cm; 160 cmd. 30 cm; 60 cm; 11.7 cm

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

36. 111

O x°

a. 291b. 69c. 55.5d. 222

37. 12

O

x°

QP

a. 78b. 39c. 102d. 24

38. is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale.

B

O

A

r

a. 9.9b. 7c. 13d. 3.6

39. , , , DF = 18 in.What is BC?

D

C

A

Z

B

F

a. 36 in.b. 18 in.c. 27 in.d. 9 in.

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

40.

6

8

x

a. 8b. 5c. 6d. 10

41. Find the measure of BAC. (The figure is not drawn to scale.)

A

C

O

B

57º

a. 57b. 28.5c. 33d. 114

42. Find the measures of the indicated angles. Which statement is NOT true? (The figure is not drawn to scale.)

O

a bc

d

a. a = 53b. b = 106c. c = 73d. d = 37

43. In the circle, . Find m BCP. (The figure is not drawn to scale.)

A

D

C

B

P

Q

a. 49b. 98c. 196d. 82

44. and . Find m A. (The figure is not drawn to scale.)

D

A

E

C

B

a. 32.5 b. 65 c. 95.5 d. 96.5

45.Find the value of x for and . (The figure is not drawn to scale.)

C

A

D

B

O

x

a. 35.5b. 58.5c. 71d. 21

46. Write the standard equation of the circle in the graph.

O 4 8–4–8 x

4

8

–4

–8

y

a. (x + 3) + (y – 2) = 9b. (x – 3) + (y + 2) = 9c. (x – 3) + (y + 2) = 18d. (x + 3) + (y – 2) = 18

47. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

10

8

15x

a. 18.8b. 120c. 5.3d. 12

Write the standard equation for the circle.48. center (–6, 9), r = 3

a. (x – 9) + (y + 6) = 9b. (x + 6) + (y – 9) = 3c. (x – 6) + (y + 9) = 3d. (x + 6) + (y – 9) = 9

49. Find the center and radius of the circle with equation (x

+ 2) + (y + 10) = 4.a. center (–2, –10); r = 2b. center (2, 10); r = 4c. center (–2, –10); r = 4d. center (10, 2); r = 2

50. A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, the wheel placement (center) and radius is modeled by

the equation . What is the graph that shows the position and radius of the wheels?

a.

4 8–4–8 x

4

8

–4

–8

y

b.

4 8–4–8 x

4

8

–4

–8

y

c.

4 8–4–8 x

4

8

–4

–8

y

d.

4 8–4–8 x

4

8

–4

–8

y

Math III Geometry ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: L3REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesNAT: CC G.CO.10| CC G.CO.12| CC G.SRT.5| G.1.c| G.2.e| G.3.eSTA: NC 2.03a TOP: 4-5 Problem 2 Using AlgebraKEY: Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | isosceles triangleDOK: DOK 2

2. ANS: C PTS: 1 DIF: L3REF: 4-2 Triangle Congruence by SSS and SASOBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS PostulatesNAT: CC G.SRT.5| CC G.MG.2| G.2.e| G.3.e| G.5.e STA: NC 2.03aTOP: 4-2 Problem 1 Using SSS KEY: SSS | reflexive property | proofDOK: DOK 2

3. ANS: B PTS: 1 DIF: L4REF: 4-2 Triangle Congruence by SSS and SASOBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS PostulatesNAT: CC G.SRT.5| CC G.MG.2| G.2.e| G.3.e| G.5.e STA: NC 2.03aTOP: 4-2 Problem 2 Using SAS KEY: SAS | reasoningDOK: DOK 2

4. ANS: B PTS: 1 DIF: L2REF: 4-3 Triangle Congruence by ASA and AASOBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS TheoremNAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: NC 2.03aTOP: 4-3 Problem 1 Using ASA KEY: ASA DOK: DOK 1

5. ANS: A PTS: 1 DIF: L2REF: 4-3 Triangle Congruence by ASA and AASOBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS TheoremNAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: NC 2.03aTOP: 4-3 Problem 4 Determining Whether Triangles Are CongruentKEY: ASA | AAS | SAS DOK: DOK 2

6. ANS: A PTS: 1 DIF: L3REF: 4-3 Triangle Congruence by ASA and AASOBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS TheoremNAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: NC 2.03aTOP: 4-3 Problem 4 Determining Whether Triangles Are CongruentKEY: ASA | reasoning DOK: DOK 2

7. ANS: D PTS: 1 DIF: L3REF: 4-4 Using Corresponding Parts of Congruent TrianglesOBJ: 4-4.1 Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruentNAT: CC G.SRT.5| CC G.CO.12| G.2.e| G.3.e STA: NC 2.03aTOP: 4-4 Problem 1 Proving Parts of Triangles Congruent

KEY: ASA | corresponding parts | proof DOK: DOK 2

8. ANS: A PTS: 1 DIF: L2REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesNAT: CC G.CO.10| CC G.CO.12| CC G.SRT.5| G.1.c| G.2.e| G.3.eSTA: NC 2.03a TOP: 4-5 Problem 2 Using AlgebraKEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum TheoremDOK: DOK 2

9. ANS: D PTS: 1 DIF: L3REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesNAT: CC G.CO.10| CC G.CO.12| CC G.SRT.5| G.1.c| G.2.e| G.3.eSTA: NC 2.03a TOP: 4-5 Problem 2 Using Algebra KEY: angle bisector | isosceles triangleDOK: DOK 2

10. ANS: A PTS: 1 DIF: L4REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesNAT: CC G.CO.10| CC G.CO.12| CC G.SRT.5| G.1.c| G.2.e| G.3.eSTA: NC 2.03a TOP: 4-5 Problem 3 Finding Angle MeasuresKEY: Isosceles Triangle Theorem | isosceles triangle DOK: DOK 2

11. ANS: C PTS: 1 DIF: L3 REF: 4-6 Congruence in Right TrianglesOBJ: 4-6.1 Prove right triangles congruent using the Hypotenuse-Leg TheoremNAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: NC 2.03aTOP: 4-6 Problem 1 Using the HL TheoremKEY: HL Theorem | right triangle | reasoning DOK: DOK 1

12. ANS: A PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problemsNAT: CC G.CO.10| CC G.SRT.5| G.3.c STA: NC 2.03aTOP: 5-1 Problem 2 Finding LengthsKEY: midpoint | midsegment | Triangle Midsegment TheoremDOK: DOK 2

13. ANS: D PTS: 1 DIF: L3REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectorsNAT: CC G.CO.9| CC G.SRT.5| G.3.c TOP: 5-2 Problem 3 Using the Angle Bisector TheoremKEY: Angle Bisector Theorem | angle bisectorDOK: DOK 2

14. ANS: B PTS: 1 DIF: L3REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectorsNAT: CC G.CO.9| CC G.SRT.5| G.3.c TOP: 5-2 Problem 3 Using the Angle Bisector TheoremKEY: Converse of the Angle Bisector Theorem | angle bisectorDOK: DOK 2

15. ANS: A PTS: 1 DIF: L2 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c STA: NC 2.03a

TOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: circumcenter of the triangle | circumscribe DOK: DOK 1

16. ANS: B PTS: 1 DIF: L3 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c STA: NC 2.03aTOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: circumscribe | circumcenter of the triangle DOK: DOK 2

17. ANS: C PTS: 1 DIF: L2 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c STA: NC 2.03aTOP: 5-3 Problem 1 Finding the Circumcenter of a TriangleKEY: point of concurrency | concurrent | circumcenter of the triangle | incenter of the triangle | centroid | orthocenter of the triangle DOK: DOK 1

18. ANS: C PTS: 1 DIF: L3 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectorsNAT: CC G.C.3| G.3.c STA: NC 2.03aTOP: 5-3 Problem 3 Identifying and Using the Incenter of a TriangleKEY: angle bisector | incenter of the triangle | point of concurrencyDOK: DOK 1

19. ANS: B PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 5-4.1 Identify properties of medians and altitudes of a triangleNAT: CC G.CO.10| G.3.c TOP: 5-4 Problem 1 Finding the Length of a MedianKEY: centroid | median of a triangle DOK: DOK 1

20. ANS: D PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 5-4.1 Identify properties of medians and altitudes of a triangleNAT: CC G.CO.10| G.3.c TOP: 5-4 Problem 2 Identifying Medians and AltitudesKEY: median of a triangle DOK: DOK 1

21. ANS: B PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 5-4.1 Identify properties of medians and altitudes of a triangleNAT: CC G.CO.10| G.3.c TOP: 5-4 Problem 3 Finding the OrthocenterKEY: angle bisector | circumcenter of the triangle | centroid | orthocenter of the triangle | median | altitude | perpendicular bisector DOK: DOK 1

22. ANS: B PTS: 1 DIF: L3 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygonsNAT: CC G.SRT.5| M.1.b| M.2.f| M.3.a| G.2.e| G.3.e STA: NC 2.03c| NC 2.03bTOP: 7-2 Problem 2 Determining SimilarityKEY: similar polygons | corresponding sides | corresponding anglesDOK: DOK 2

23. ANS: D PTS: 1 DIF: L4 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Identify and apply similar polygonsNAT: CC G.SRT.5| M.1.b| M.2.f| M.3.a| G.2.e| G.3.e STA: NC 2.03c| NC 2.03bTOP: 7-2 Problem 2 Determining Similarity KEY: similar polygonsDOK: DOK 2

24. ANS: C PTS: 1 DIF: L3 REF: 7-2 Similar Polygons

OBJ: 7-2.1 Identify and apply similar polygonsNAT: CC G.SRT.5| M.1.b| M.2.f| M.3.a| G.2.e| G.3.e STA: NC 2.03c| NC 2.03bTOP: 7-2 Problem 3 Using Similar Polygons KEY: corresponding sides | proportionDOK: DOK 2

25. ANS: C PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS TheoremsNAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.eTOP: 7-3 Problem 1 Using the AA Postulate KEY: Angle-Angle Similarity PostulateDOK: DOK 2

26. ANS: A PTS: 1 DIF: L3 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS TheoremsNAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.eTOP: 7-3 Problem 2 Verifying Triangle Similarity KEY: Side-Side-Side Similarity TheoremDOK: DOK 2

27. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 Use the AA Postulate and the SAS and SSS TheoremsNAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.eTOP: 7-3 Problem 2 Verifying Triangle SimilarityKEY: Side-Angle-Side Similarity Theorem | corresponding sidesDOK: DOK 2

28. ANS: A PTS: 1 DIF: L4 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Use similarity to find indirect measurementsNAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.e| G.5.eTOP: 7-3 Problem 4 Finding Lengths in Similar TrianglesKEY: Angle-Angle Similarity Postulate | word problem DOK: DOK 2

29. ANS: D PTS: 1 DIF: L4 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Find and use relationships in similar trianglesNAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.eTOP: 7-4 Problem 2 Finding the Geometric Mean KEY: geometric mean | proportionDOK: DOK 2

30. ANS: B PTS: 1 DIF: L3 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Find and use relationships in similar trianglesNAT: CC G.SRT.5| CC G.GPE.5| G.2.e| G.3.eTOP: 7-4 Problem 3 Using the CorollariesKEY: corollaries of the geometric mean | proportion DOK: DOK 2

31. ANS: A PTS: 1 DIF: L4 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector TheoremNAT: CC G.SRT.4| CC G.SRT.5| N.4.c| M.3.aTOP: 7-5 Problem 1 Using the Side-Splitter Theorem KEY: Side-Splitter TheoremDOK: DOK 2

32. ANS: A PTS: 1 DIF: L4 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector TheoremNAT: CC G.SRT.4| CC G.SRT.5| N.4.c| M.3.a TOP: 7-5 Problem 2 Finding a LengthKEY: corollary of Side-Splitter Theorem DOK: DOK 2

33. ANS: A PTS: 1 DIF: L3 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Use the Side-Splitter Theorem and the Triangles Angle-Bisector TheoremNAT: CC G.SRT.4| CC G.SRT.5| N.4.c| M.3.aTOP: 7-5 Problem 3 Using the Triangle-Angle-Bisector TheoremKEY: Triangle-Angle-Bisector Theorem DOK: DOK 2

34. ANS: A PTS: 1 DIF: L3 REF: 10-6 Circles and ArcsOBJ: 10-6.1 Find the measures of central angles and arcsNAT: CC G.CO.1 STA: NC 1.02 TOP: 10-6 Problem 2 Finding the Measures of ArcsKEY: major arc | measure of an arc | arc DOK: DOK 1

35. ANS: A PTS: 1 DIF: L4 REF: 10-6 Circles and ArcsOBJ: 10-6.2 Find the circumference and arc length NAT: CC G.CO.1STA: NC 1.02 TOP: 10-6 Problem 4 Finding Arc LengthKEY: circumference | radius DOK: DOK 2

36. ANS: B PTS: 1 DIF: L3 REF: 12-1 Tangent LinesOBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2| G.3.hSTA: NC 2.03d TOP: 12-1 Problem 1 Finding Angle MeasuresKEY: tangent to a circle | point of tangency | properties of tangents | central angleDOK: DOK 1

37. ANS: A PTS: 1 DIF: L3 REF: 12-1 Tangent LinesOBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2| G.3.hSTA: NC 2.03d TOP: 12-1 Problem 1 Finding Angle MeasuresKEY: tangent to a circle | point of tangency | angle measure | properties of tangents | central angle DOK: DOK 1

38. ANS: B PTS: 1 DIF: L3 REF: 12-1 Tangent LinesOBJ: 12-1.1 Use properties of a tangent to a circle NAT: CC G.C.2| G.3.hSTA: NC 2.03d TOP: 12-1 Problem 3 Finding a RadiusKEY: tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem

DOK: DOK 2

39. ANS: B PTS: 1 DIF: L3 REF: 12-2 Chords and ArcsOBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2| G.3.hSTA: NC 2.03d TOP: 12-2 Problem 2 Finding the Length of a ChordKEY: circle | radius | chord | congruent chords | bisected chordsDOK: DOK 1

40. ANS: D PTS: 1 DIF: L2 REF: 12-2 Chords and ArcsOBJ: 12-2.2 Use perpendicular bisectors to chords NAT: CC G.C.2| G.3.hSTA: NC 2.03d TOP: 12-2 Problem 3 Using Diameters and ChordsKEY: bisected chords | circle | perpendicular | perpendicular bisector | Pythagorean TheoremDOK: DOK 2

41. ANS: B PTS: 1 DIF: L3 REF: 12-3 Inscribed AnglesOBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4| G.3.hSTA: NC 2.03d TOP: 12-3 Problem 1 Using the Inscribed Angle TheoremKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 1

42. ANS: C PTS: 1 DIF: L4 REF: 12-3 Inscribed AnglesOBJ: 12-3.1 Find the measure of an inscribed angle NAT: CC G.C.2| CC G.C.4| G.3.h

STA: NC 2.03d TOP: 12-3 Problem 2 Using Corollaries to Find Angle MeasuresKEY: circle | inscribed angle | intercepted arc | inscribed angle-arc relationshipDOK: DOK 2

43. ANS: A PTS: 1 DIF: L2 REF: 12-3 Inscribed AnglesOBJ: 12-3.2 Find the measure of an angle formed by a tangent and a chordNAT: CC G.C.2| CC G.C.4| G.3.h STA: NC 2.03d TOP: 12-3 Problem 3 Using Arc MeasureKEY: circle | inscribed angle | tangent-chord angle | arc measure | angle measureDOK: DOK 1

44. ANS: A PTS: 1 DIF: L3REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2| G.3.h STA: NC 2.03dTOP: 12-4 Problem 1 Finding Angle MeasuresKEY: circle | secant | angle measure | arc measure | intersection outside the circleDOK: DOK 1

45. ANS: A PTS: 1 DIF: L3REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.1 Find measures of angles formed by chords, secants, and tangentsNAT: CC G.C.2| G.3.h STA: NC 2.03dTOP: 12-4 Problem 1 Finding Angle MeasuresKEY: circle | secant | angle measure | arc measure | intersection inside the circleDOK: DOK 1

46. ANS: B PTS: 1 DIF: L3REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.1 Write the equation of a circle NAT: CC G.GPE.1| G.3.h| G.4.a| G.4.fSTA: NC 2.03d TOP: 12-5 Problem 1 Writing the Equation of a CircleKEY: center | circle | coordinate plane | radius | equation of a circleDOK: DOK 2

47. ANS: D PTS: 1 DIF: L3REF: 12-4 Angle Measures and Segment LengthsOBJ: 12-4.2 Find the lengths of segments associated with circlesNAT: G.3.h STA: NC 2.03d TOP: 12-4 Problem 3 Finding Segment LengthsKEY: circle | chord | intersection inside the circle DOK: DOK 2

48. ANS: D PTS: 1 DIF: L3REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.1 Write the equation of a circle NAT: CC G.GPE.1| G.3.h| G.4.a| G.4.fSTA: NC 2.03d TOP: 12-5 Problem 1 Writing the Equation of a CircleKEY: equation of a circle | center | radius DOK: DOK 1

49. ANS: A PTS: 1 DIF: L3REF: 12-5 Circles in the Coordinate PlaneOBJ: 12-5.2 Find the center and radius of a circle NAT: CC G.GPE.1| G.3.h| G.4.a| G.4.fSTA: NC 2.03d TOP: 12-5 Problem 1 Writing the Equation of a CircleKEY: center | circle | coordinate plane | radius DOK: DOK 2

50. ANS: A PTS: 1 DIF: L3

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