Geometry Cc Wrkbk Anskey 1st Edition View Only

7/23/2019 Geometry Cc Wrkbk Anskey 1st Edition View Only

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C

Edition

Core

ommon

eometryorkbookW

G

Topical Review Book Company

Standards

Answer Key


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3/20

TEST 1Part I

1. 2 5. 4 9. 2 13. 1 17. 2 21. 32. 4 6. 3 10. 3 14. 2 18. 4 22. 33. 1 7. 2 11. 2 15. 3 19. 1 23. 24. 3 8. 4 12. 4 16. 4 20. 3 24. 4

For parts II, III, and IV, answers may vary, partial credit should be given

for answers that include, but not limited to, the following;

- correct answer, but no work shown

- incorrect answer, but rest of work is appropriate

- appropriate work is shown, but one computational or rounding

error is made

Part II25.

26. Yes, by SSS

27. a) b)A(5, 4) B(10, 4) C(11, 0) D(6, 0)

28. The container can hold approximately 4189 cubic centimeters of ice cream.

29. S.A. = 480 square units

y

x

7

6

54

3

2

1

0

-1

-2

-3

B

C

A

D

B A

C D-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4

P

Q

P

Q


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30.

31. 125

32.Statement Reason

1. LMNOis a parallelogram 1. Given MOis a diagonal ofLMNO

2. LM ||NOandLO||MN 2. Denition of parallelogram

3. OMLMON 3. Alternate interior angles are congruent LOM NMO

4. MOMO 4. Reexive property

5. DMOLDMON 5. ASA

6. LMNO and MNLO 6. Corresponding parts of congruenttriangles are congruent

Part III

33. Possible response isT(2, 1)andRy-axis

34. a)

b) Yes, DABCand DDEFwould be congruent by SAS.

y

x

543210

-1-2-3

D

F EB C

A

Figure 1 Figure 2l

((

LL

MN

M

A B

N


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35. a) Perimeter using the distance formula is approximately 24 units or 240 feet.

b) Cost: $2388.00

Note:PointDon the Property Diagram, in the book, should be at (7, 7) and

not at (8, 7).

36.

Part IV

37. Statement Reason1.ABCDis a parallelogram. 1. Given

EFbisect ABatE.

EFbisects CDatF

2. AB CD& AB||CD 2. Opposite sides of a parallelogram are and ||.

3. EB EA& FDFC 3. Denition of bisector

4. EB FD

4. If equal quantities are divided equally, theresults are equal.

5. GBE GDFand 5. When parallel lines are cut by a transversal,

BEG DFG alternate interior angles are congruent.

6. DBEG DDFG 6.ASA

7. EGFG 7.Corresponding Parts of Congruent Triangles

are Congruent


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TEST 2Part I

1. 1 5. 4 9. 3 13. 3 17. 3 21. 22. 4 6. 3 10. 3 14. 3 18. 3 22. 33. 3 7. 3 11. 2 15. 4 19. 4 23. 14. 2 8. 1 12. 1 16. 1 20. 2 24. 2






error is made

Part II

25. Yes, for example,AC=BC=3 5 and appropriate justication.

26.

27. 8.4 square inches

28.

29.

Statement Reason

1. Isosceles DABC, bisector AD 1. Given

2. AB AC 2. Denition of isosceles triangle

3. AD AD 3. Reexive property

4. BD DC 4. Denition of perpendicular as bisector

5. DADB DADC 5. SSS

6.


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31.

32. The volume of the cylinder is three times the volume of the cone, or the

volume of the cone is 1/3the volume of the cylinder.

Part III

33.

a) Use slope to prove that bothpair of opposite sides of thequadrilateral are parallel.

m

m

BC AD

BC

AD

=

=

4

5

4

5

m

m

AB DC

AB

DC

=

=

5

4

5

4

ABCDis a parallelogram because

it is a quadrilateral with two pairof parallel sides.

b) From the slope values found in part a, AB BCbecause their slopes arenegative reciprocals of each other. Since perpendicular lines form rightangles,ABCDcontains a right angle and is a rectangle.

34. a) Use the construction of a perpendicular bisector of each side to nd the midpoint. Connect each vertex to the midpoint of the opposite side to construct the

the medians.

b) 1 point of intersection

y

x

B(-2, 3)

A(-6, -2)

D(-1, -6)

C(3, -1)

P

Q

R

TBA

C

||||


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35. The diagonals of the quadrilaterals are congruent because they are bothdiameters of the circle. They are perpendicular by construction. A quadrilateralwith congruent perpendicular diagonals is a square.

A=1

2

bh

A=1

2(12.5)2

A= 78.125 sq inches

A= 4(78.125)

A= 312.5 sq inches

36. a) The constant of dilation (scale factor) is 2.

b) The constant of dilation gives the similarity ratio between thetwo triangles.

Part IV

37. a) translation (x 3,y+ 2)

b) Reection in they-axis

c) Rotation of 90 degrees about the origin

d) Yes, each of the transformations is a rigid motion, so the two triangleswould be congruent.

e) A dilation of 2 would result in a triangle that would not be congruentto DABCbecause the size of the triangle would change.

A

B C

y

x

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11

65

4

3

2

1

0

-1

-2

-3

-4

-5

-6

A

B

C

A

B

C

B

C

A


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TEST 3Part I

1. 2 5. 3 9. 1 13. 1 17. 1 21. 32. 1 6. 2 10. 1 14. 4 18. 2 22. 23. 4 7. 4 11. 1 15. 3 19. 1 23. 24. 3 8. 1 12. 2 16. 3 20. 3 24. 1






error is made

Part II

25. S. A. = 80 square units26. No, for example cosBis always equal to sinA

cosB=BC

ABand sinA=

BC

AB.

27. V = 46,166

28.

Example Plan: Show that AD BC;ABDC, and that AD DC.

d

d

AD

BC

= ( ) + ( ) = + = =

= + ( )

1 1 4 1 0 3 9 3

5 5 1 4

2 2 2 2

2

( ) ( ) ( )

( ) ( ) 22 2 2

2 2 2 2

0 3 9 3

1 5 1 1 6 0 36 6

5

= + = =

= + ( ) = + = =

=

AD BC

d

d

AB

DC

( ) ( )

( 11 4 4 6 0 36 6

1 1

1 4

0

3

2 2 2 2) ( )

( )

( )

( ) + ( ) = + = =

=

=

=

AB DC

m

m

AD

DC55 1

4 460

=( )

( ) : .Undefined

\AD DCbecause they have slopes that are negativereciprocals of each other.

Conclusion:ABCDis a rectangle because it is a quadrilateral in whichboth pair of opposite sides are congruent and a pair of adjacent sides thatis perpendicular.

y

x0-1-2-3-4

-5

-3 -2 -1 1 2 3 4 5 6 7 8 9

B

C

A

D


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29. Yes, by ASA

30.

31.

32. a) 112 security guards b) 110 people

Part III33. d

C D' '= 2a

34. Reection: (x,y) (x, y) (Reection over thex-axis)

Followed by Translation: (x,y) (x+ 5,y+ 1)Triangle 2 labels: A(0, 6),B(3, 4) and Cis at (2, 2)

D1 D2 because reections and translations are rigid motion and preserve angle measure and distance.

S

O

U

T

y

x

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

1

A

C

2

B

B

A

C


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35.AB

=AD

AB =

AD AD + DC =AC

AC AB AC BC

(AB)2= (AC)(AD) (BC)2= (AC)(DC)

(AB)2+ (BC)2= (AC)(AD) + (AC)(DC)

(AB)2

+ (BC)2

=AC(AD+DC) (AB)2+ (BC)2=AC(AC)

(AB)2+ (BC)2= (AC)2

36. a) and b)

c) ry-axis

Part IV

37. a) cone b) 44 gallons more

y

x

Y

Z

X

Z

Y

X


12/20

TEST 4Part I

1. 4 5. 3 9. 1 13. 4 17. 4 21. 22. 4 6. 3 10. 2 14. 4 18. 2 22. 13. 2 7. 4 11. 3 15. 2 19. 2 23. 24. 1 8. 2 12. 2 16. 3 20. 1 24. 3






error is made

Part II

25. S1= 67.08 and S2= 33.54

26. x= 3 andy= 2

27.

28.

29. T3,5then a Rot180

30. The side opposite the longest angle is not the longest side.Therefore the triangle drawn is not plausible.

31. Rot360and reection across line of symmetry

32. a) possible answers may include a square, triangle, rectangle, pentagon,and hexagon

b) possible answers include a circle or octagon


13/20

Part III

33. 7.6 units

34. a)AB= 41 b)

c) (x 3)2+y2= 41

35. Area = 12 square units

36. a)

b)y =3

2

x+ 1 or equivalent response.

Part IV

37. a) and b)

c)Aequation is (x 4)2+ (y+ 7)2= 4 Aequation is (x 4)2+ (y+ 7)2= 16

y

x

-2 -1 1 2 3 4 5 6 7 8 9 10

1

0

-1

-2

-3-4-5-6-7-8-9

-10-11-12

y

x

7

6

5

4

3

2

10

-1

-2

-3

-4

-5

-6

-7

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

A

B

y

x

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

B

CA

A

A

A


14/20

TEST 5Part I

1. 3 5. 1 9. 1 13. 2 17. 1 21. 22. 4 6. 2 10. 1 14. 3 18. 1 22. 23. 2 7. 3 11. 1 15. 2 19. 1 23. 34. 2 8. 4 12. 3 16. 4 20. 3 24. 1






error is made

Part II

25. 12026. The third side has to be longer than 4 cm and shorter than 24 cm.

27. Distance from (0, 0) to (1, 3 ) = 2 Distance from (0, 0) to (0, 2) = 2 Therefore, the point (1, 3 ) lies on the circle centered at the origin

and containing the point (0, 2).

28. 972m3

29. Statement Reason

1.AB|| CD,EFintersects ABand 1. Given

CDatPand Trespectively.

2.xCTP 2. When 2 lines are cut by a transversalcorresponding angles are congruent.

3.CTP+ yare supplementary. 3. Two angles that form a straight line are supplementary. (Or linear pairs

of angles are supplementary.

4.x+ yare supplementary. 4. Substitution

30. a) b)ABCDrx-axis ABCD

ABCDt0, 3 ABCD

y

x

-4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10B

CA

D

9

8

7

6

5

4

3

21

0

-1

-2

-3

-4

-5

-6

AB

C

D

A

D

C

B

(7, 8)

(7, 5)

(7, 5)

(7, 2)

(4, 5)

(5, 4)

(4, 2)(5, 1)


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y

x

--8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8

A

B

C

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

C

B A A

B

C

31. Yes, by SAS. DABC DCDA

32. 3 + 13 + 2 2 + 2 5

33.

34. 133 inches

35. a)

b) Rot180

36.

37.

Statement Reason

1. AB || EDand Cis the 1. Givenmidpoint of AD.

2. BAC EDC 2. If 2 parallel lines are cut by a transversal,

the alternate interior angles are congruent.

3. AC DC 3. Denition of midpoint

4. ACB DCE 4. Vertical angles are congruent.

5. DABC DDEC 5.ASA ASA

6. DE AB 6. Corresponding parts of congruent triangles

are congruent.


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TEST 6Part I

1. 2 5. 2 9. 3 13. 2 17. 4 21. 42. 1 6. 1 10. 4 14. 1 18. 3 22. 23. 1 7. 1 11. 3 15. 4 19. 2 23. 14. 3 8. 4 12. 3 16. 1 20. 3 24. 3






error is made

Part II

25.Statement Reason

1. LO NQ& LPNP 1. Given

and PL NP

2. PRight angle 2. Perpendicular lines form right angles.

3. P P 3. Refexive property

4. DQPN& DOPLare 4. A triangle containing a right angle

right triangles is a right triangle.

5. DQPNDOPL 5. HLHL

QPOP

6. Corresponding parts of congruent6. triangles are congruent

26.

Statement Reason

1. mRSU+ mRST= 180 1. Linear angle pairs are supplementary

2. mRST+ mTSV= 180 2. Linear angle pairs are supplementary

3. mRSU+ mRST= mRST+ mTSV 3. Substitution

4. mRSUmTSV 4. Subtraction

27.

28. (4.8, 1)


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29.

30.

a) d

d

AD

AB

= + + + = + = =

= + + = + = =

( ) ( )

( ) ( )

1 4 1 2 9 9 18 3 2

1 3 1 3 16 16 32 4 2

2 2

2 2

PP l w

P

A lw

A

A

= +

= +( ) =

=

= ( )( )=

2 2

2 3 2 4 2 14 2

3 2 4 2

24

b)

31. a) Similar

b) Example: A dilation with a constant of dilation of would create theimage. In a dilation the angles are preserved, but distance is changed

by the factor of the constant of dilation. If 2 angles on a triangle to2 corresponding angles in another, the triangles are similar.

32. 3 13+ 5

A

B

A

B

y

x

A(1, 1)

D

(4, 2)B(3, 3)

C

(0, 6)


18/20

Part III

33. Jessicas container; .3125 g/cubic inch vs .2381 g/cubic inch

34. a)

b) S (7, 3) T (13, 3) U (11, 6) V (5, 6)

c) S (7, 3) T (13, 3) U (11, 6) V (5, 6)

35. Midpoint of WY= midpoint of XZ= (1, 5

2).

Since the diagonals of WXYZshare the same midpoint, they bisect eachother. Therefore WXYZis a parallelogram.

WY = 13 XZ= 101 WY XZ(should be not congruent).

Since the diagonals of WXYZare not congruent, it is not a rectangle.

36.

y

x

7

6

5

4

3

2

1

0

-1

-2

-3-4

-5

-6

-7

S T

V

U

-4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14

S

T

V

U

S

V

U

T

B

C

D

E

B

D

E

C

center


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Part IV

37.

Statement Reason

1. m1 m2 1. Given

AEbisects BD 2. BC DC 2. Denition of bisector

3. DEC and 2 are supplementary. 3. They are linear pairs.

BAC and 1 are supplementary.

4. If two angles are each supplementary4. DEC BAC to the same or equal angles, they are

congruent to each other.

5. BCA DCE 5. Vertical angles are congruent

6. DACB DECD 6. AASAAS

7.AB

DE 7. Corresponding parts of congruenttriangles are congruent. (CPCTC)


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Geometry Cc Wrkbk Anskey 1st Edition View Only

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