practice workbook - · pdf filepractice workbook to jump to a location in this book 1. ... 1 0...

Practice Workbook

To jump to a location in this book

1. Click a bookmark on the left.

To print a part of the book

1. Click the Print button.

2. When the Print window opens, type in a range of pages to print.

The page numbers are displayed in the bar at the bottom of the document. In the example below,“1 of 151” means that the current page is page 1 in a file of 151 pages.

For Exercises 1–4, refer to the triangle at right.

1. Name all the segments in the triangle.

2. Name each of the angles in the triangle by using three differentmethods.

3. Name the rays that form each of the angles of the triangle.

4. Name the plane that contains the triangle.

State whether each object could best be modeled by a point, line, or plane.

5. a star 6. a notebook cover

7. a ruler edge 8. the tip of a pen

9. a sheet of paper 10. a letter opener

Classify each statement as true or false, and explain your

reasoning in each false case.

11. Two planes intersect in only one point.

12. A ray starts at one point on a line and goes on forever.

13. The intersection of two planes is one line.

For Exercises 14–18, T is the midpoint of . Classify each

statement as true or false.

14. C, T, and B are collinear.

15. is the same as .

16. C, T, and B name a plane.

17. R, T, and C are collinear.

18. Four rays start at T.

RT←→

RS←→

BC

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.

Geometry Practice Workbook 1

Practice

1.1 The Building Blocks of Geometry

NAME CLASS DATE

Q

R S

1

32

B

R C

S

T

In Exercises 1–4, find the segment lengths determined by the

points on the number line.

1. RV � 2. TX �

3. SW � 4. VW �

5. The length of a segment must be a positive number. Explain why the order of the coordinates does not matter when calculating length.

Name all of the congruent segments in each figure.

6.

7.

Point B is between points Q and R on . Sketch a figure

for each set of values, and find the missing lengths.

8. QB � 20; BR � 10; QR �

9. QB � 50; BR � ; QR � 110

10. QB � ; BR � 16.9; QR � 51.5

Find the indicated values.

11. AC � 45; x �

12. DF � 135; x �

QR

L

S

Q

R

P

M

N O

A B D

–3 –2 –1 0 1 2 3

C

R

–6

S T U V W X

–5 –4 –3 –2 –1 0 1 2 3 4 5 6

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.

2 Practice Workbook Geometry

Practice

1.2 Measuring Length

NAME CLASS DATE

30x

A B C

110x

D E F

Find the measure of each angle in the diagram

at right.

1. m�SVR

2. m�SVQ

3. m�SVP

4. m�RVQ

5. m�PVR

6. Name all sets of congruent angles in the diagram below.

Find the missing angle measures.

7. m�BTE � 40�, m�ETM � 60�, m�BTM �

8. m�BTE � 112�, m�ETM � , m�BTM � 168�

9. m�BTE � , m�ETM � 47�, m�BTM � 92�

In the figure at right, m�CED � 39�, m�CEL � (3x � 6)�, and

m�LED � (x � 25)�.

10. What is the value of x?

11. What is m�CEL?

In the diagram at right, m�DSF � (45 � x)�. Find the value

of x, and then give each indicated angle measure.

12. m�DSF 13. m�DSE 14. m�ESF

95°S

170°

65°

30°

Z

W

B

1 2 3 4 5

1 2 3 4 5 6 7 8 9 1 0cm

90

90

100

80

11070

12060

13050

14040

16020

10

170

20160

30150

40140

50

13060

12070

11080

100

17010

15030

125°P

0°A

V

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

1.3 Measuring Angles

NAME CLASS DATE

1 2 3 4 5

1 2 3 4 5 6 7 8 9 1 0cm

160°

100°70°

40°

P

Q R

S90

90

100

80

11070

12060

13050

14040

16020

10

170

20160

30150

40140

50

13060

12070

11080

100

17010

15030

V

M

B E

T

D

C L

E

SE

D

F

5x + 4

4x + 1

Construct all of the geometric figures below by folding a sheet

of paper.

1. Describe how to construct a line, �, through points C and D.

2. Describe how to construct two lines perpendicular to line �from Exercise 1, line m through point D and line p through point C.

3. Describe the relationship between lines m and p.

4. Write a conjecture about the number of lines perpendicular to line � that can be constructed.

5. Describe how to construct a segment bisector, r, of .

6. Describe line r in relation to .

7. Write a conjecture about the number of perpendicular bisectors of that can be constructed.

8. How can you determine whether a given line is the angle bisector of an angle?

CD

CD

CD

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

1.4 Exploring Geometry by Using Paper Folding

NAME CLASS DATE

C

D

C

D

p

m

�

C

D

p

m

�

E

r

In Exercises 1–4, trace the given triangle on folding paper or sketch it

with geometry software. Then construct the indicated geometric figures.

1. the perpendicular bisectors 2. the angle bisectors of each of the sides of ∆GHI angle in ∆PQR

3. the circumscribed circle of ∆JKL 4. the inscribed circle of ∆MNO

For Exercises 5–7, draw or fold an acute triangle, with all angles

measuring less than 90�; and a right triangle, with one angle

measure of 90�.

5. Construct the circumcenter of the right triangle and use it to drawits circumscribed circle.

6. Construct the centroid of an acute triangle and label it point C.

7. How many line segments with endpoint C are formed from themedians in Exercise 6? Describe the relationships among thesesegments.

Complete each statement with always, sometimes, or never.

8. A median of a triangle contains a vertex and the midpoint of the

opposite side.

9. An altitude is perpendicular to the opposite side.

10. An altitude is an angle bisector.

M

O

N

LJ

K

Q

R

P

H

I

G

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

1.5 Special Points in Triangles

NAME CLASS DATE

Identify each rigid motion as a reflection, translation, or rotation.

1. 2. 3.

In the diagram at right, point D is shifted

3 cm in the direction shown to form point D� .

4. Describe how point E� was formed.

5. Given any point of ∆DEF, tell how to locate its image point in∆D�E�F�.

Reflect each figure across the given line.

6. 7. 8.

Reflect the word TOT across each line.

9. 10. 11.

TOT

image

image

image

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

1.6 Motion in Geometry

NAME CLASS DATE

E

D F

E'

D' F'

Use the given rule to translate each triangle on the grid provided.

1. H(x, y) � (x, y � 3) 2. H(x, y) � (x, �y)

3. H(x, y) � (x � 4, y) 4. H(x, y) � (x � 2, y � 1)

Describe the result of applying each rule below to a figure in a

coordinate plane.

5. G(x, y) � (x � 6, y) 6. F(x, y) � (x, y � 1)

7. P(x, y) � (x, �y) 8. H(x, y) � (�x, y)

9. T(x, y) � (x � 4, y � 5) 10. R(x, y) � (x � 2, y � 2)

11. M(x, y) � (x � 5, y � 2) 12. N(x, y) � (�x, �y)

x

y

O 1

1

x

y

O 1

1

x

y

O 1

1

x

y

O 1

1

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

1.7 Motion in the Coordinate Plane

NAME CLASS DATE

How many line segments can be drawn between 3, 4, 5,

and 6 points? Draw them. Then record your data in the

table. (Note: The points are noncollinear—that is, they

are not on the same line.)

1. 2.

3. 4.

5. What is the pattern?

6. If the pattern continues, how many line segments can be drawn

between 10 noncollinear points?

7. Write an expression in terms of n for the number of line segments

that can be drawn between n points.

Logical arguments that ensure true conclusions are called proofs.

8. Consider the following conjecture: Opposite sides of aparallelogram are equal in measure. Test the conjecture bymeasuring the sides of the parallelogram at right. Record yourresults in the table.

9. Did the conjecture seem to be true? Explain.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

2.1 An Introduction to Proofs

NAME CLASS DATE

Number of Number ofPoints Line Segments

2

3

4

5

6

7

8

9

Z Y

XW

WX ZY WZ XY

Refer to the following statement to answer Exercises 1–4:

All turtles are reptiles.

1. Rewrite the statement as a conditional.

2. Identify the hypothesis and the conclusion of the statement.

3. Draw an Euler diagram that illustrates the statement.

4. Write a converse of the statement and construct its Euler diagram.If the converse is false, illustrate this with a counterexample.

5. Write a conditional statement with the given hypothesis andconclusion, and then write the converse of that statement. Is theoriginal statement true? The converse? If either is false, give acounterexample.

hypothesis: EF � DGconclusion: The diagonals of a rectangle are equal in length.

6. Arrange the three statements below into a logical chain. Then writethe conditional statement that follows from the logic.If it is warm, then it is spring.If flowers are blooming, then it is warm.If you see bees, then flowers are blooming.

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

2.2 Introduction to Logic

NAME CLASS DATE

F G

ED

Write the given sentence in the forms requested. State in your

conclusion whether the biconditional statement is true. If it is

false, state which part makes it false.

1. I am a high school sophomore in the 10th grade.

Conditional statement:

Converse:

Biconditional:

Conclusion:

2. A diamond can cut glass.


Converse:

Biconditional:

Conclusion:

3. A 130° angle is an acute angle.


Converse:

Biconditional:

Conclusion:

These figures are hexagons. These figures are not hexagons.

4. Which of the following are hexagons?

5. Write a definition for a hexagon.

c. d.a. b.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

2.3 Definitions

NAME CLASS DATE

Identify the properties of equality that justify the conclusion.

1. x � 9 � 16 Given

x � 9 � 9 � 16 � 9x � 7 Simplify

2. �B � �C ; �C � �D Given

�B � �D

3. Given

4. AB � CD Given

AB � BC � BC � CDAC � BD Segment Addition Postulate

Complete the proofs below.

5. Given: m�HGK � m�JGLProve: m�1 � m�3

6. Given: �ABC � �EFG�1 � �3

Prove: �2 � �4

CD � AB

AB � CD

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

2.4 Building a System of Geometry Knowledge

NAME CLASS DATE

32

1

GL

K

J

H

12

A

DC

43

G

HE

FB

Statements Reasons

m�HGK � m�JGL Given

Statements Reasons

�ABC � �EFG Given(m�ABC � m�EFG)

�1 � �3 (m�1 � m�3)

In the figure at right, write the angle congruent to each given angle.

1. �CSE 2. �CSF 3. �BSE

Find m�ABC.

4. 5.

m�ABC � m�ABC �

Find the value of x.

6. 7.

x � x �

Complete the proof below.

Given: �B � �C, �A is a complement of �B,and �D is a complement of �C.

Prove: �A � �D

Statements Reasons

�A and �B are complementary; �C and Given�D are complementary; m�B � m�C.

m�A � m�B � 90�; m�C � m�D � 90� 8.

m�A � m�B � m�C � m�D 9.

m�A � m�B � m�B � m�D 10.

Therefore, m�A � m�D (�A � �D) 11.

Q

S

T

U

VR

(10x)°(120 – 6x)°

(x + 40)°

(3x – 60)°

D E

BA

C

G

F

A

B

C

D

E

55°25°

A E

B

C D

75°

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

2.5 Conjectures that Lead to Theorems

NAME CLASS DATE

S

C BE

FD

A

A B DC

Draw all of the axes of symmetry for each figure.

1. 2. 3.

Each figure below shows part of a shape with reflectional

symmetry. Complete each figure.

4. 5. 6.

Each figure below shows part of a shape with the given

rotational symmetry. Complete each figure.

7. 6-fold 8. 4-fold 9. 10-fold

Examine each figure below. Identify the type of polygon. Describe

all of its symmetries. If it is regular, find the central angle measure.

10. 11. 12.

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

3.1 Symmetry in Polygons

NAME CLASS DATE

Use your conjectures about quadrilaterals from Activities 1–4 in

the textbook to find the indicated measurements.

In parallelogram GRAM, MO � 10, MA � 16,

m�GMA � 75°, and m�MRG � 35°.

1. m�GRA 2. m�MGR

3. RO 4. GR

5. m�RMA 6. m�GMO

In rhombus ABCD, AB � 6, AC � 8, and m�ABC � 30°.

7. m�ADC 8. m�AEB

9. BC 10. AE

11. m�BAD 12. m�CED

13. CD 14. EC

In rectangle FGHI, FG � 8, FI � 15, and FH � 17.

15. HI 16. GH

17. GI 18. FJ

19. GJ 20. m�FIH

In square WXYZ, WX � 20 and WY � 28.3.

21. XY 22. XZ

23. m�WVX 24. m�XYV

25. In parallelogram KLMN, m�K � (3x)° and m�L � (2x � 5)°.Find x and the measure of each angle in KLMN.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

3.2 Properties of Quadrilaterals

NAME CLASS DATE

A

G

M

R

O

B

C

D

A

E

F G

J

HI

W X

V

YZ

In the figure at right, lines � and p are parallel.

1. List all the angles that are congruent to �1.

2. List all the angles that are congruent to �2.

3. If m�1 � 115°, find the measure of each angle in the figure.

4. If m�3 � (3x)° and m�7 � (4x � 24)°, find the measure of eachangle in the figure.

For Exercises 5– 8, refer to the diagram below. Lines m and n are

parallel. Name all angles congruent to the given angle, and give

the theorems or postulates that justify your answer.

5. �6

6. �8

7. �5

8. �7

In �KLM, and �KNO � �KON. Find the indicated angle

measures.

9. m�KNO 10. m�KON

11. m�NOL 12. m�LNO

13. m�MNL 14. m�KLN

NO �ML

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

3.3 Parallel Lines and Transversals

NAME CLASS DATE

2

43

p

1

6

87

5

�

24

3

m n

1

68

75

22°44°

92°

M L

K

ON

For Exercises 1–5, refer to the diagram below, and fill in the name

of the appropriate theorem or postulate.

1. If m�5 � m�4, then � �m by the converse of the

.


.


.

4. If m�1 � m�8, then � �m by the converse of the .

5. If m�6 � m�7 � 180°, then � �m by the converse of the .

For Exercises 6–12, use the diagram at right to

complete the two-column proof below.

Given: m�1 � m�3p�q

Prove: � �m

Statements Reasons

p�q 6.

�1 and �2 are supplementary. 7.

m�1 � m�2 � 180° 8.

m�1 � m�3 9.

m�3 � m�2 � 180° 10.

�3 and �2 are supplementary. 11.

� �m 12.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

3.4 Proving That Lines Are Parallel

NAME CLASS DATE

1

5

2

6

3

7

4

8

m�

1 2

3 m

qp

�

Find the indicated angle measure for each triangle.

1. 2. 3.

m�ABC m�EDF m�RQS

For Exercises 4–11, refer to the diagram below, in which

, m�KNO � 45°, and m�KLM � 35°.

4. m�KLP 5. m�K

6. m�KON 7. m�ONM

8. m�NOL 9. m�KOP

10. m�MLP 11. m�P

For Exercises 12–17, refer to the triangle at right.

m�1 m�2 m�3 m�4 m�1 � m�2

12. 35° 60°

13. 70° 120°

14. 58° 72°

15. 43° 55°

16. 45° 85°

17. What do you notice about the relationship between m�4 and thesum of m�1 � m�2? What theorem describes this relationship?

In �ABC, m�A � (3x � 10)�, m�B � (2x � 5)�, and

m�C � (x � 9)°. Find the indicated values.

18. x � 19. m�A � 20. m�B � 21. m�C �

NP �LM, PL �KM

R

Q S

80°

55°D

E

F

130°

15°

A

B

C25°

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

3.5 The Triangle Sum Theorem

NAME CLASS DATE

K

N

M L

PO45°

35°

3

R

QS

1

2

4

Find the unknown angle measures.

1. 2. 3.

For each polygon, determine the measure of an interior angle and

the measure of an exterior angle.

4. a square 5. a regular nonagon

6. an equiangular triangle 7. an equiangular hexagon

For Exercises 8–11, an interior angle measure of a regular polygon

is given. Find the number of sides of the polygon.

8. 120° 9. 90°

10. 168° 11. 144°

For Exercises 12–15, an exterior angle measure of a regular

polygon is given. Find the number of sides of the polygon.

12. 40° 13. 120°

14. 18° 15. 60°

Find each angle measure of trapezoid ABCD.

16. �A

17. �B

18. �C

19. �D

80° 80°

?

110°

120°

?

115° 65°

65°?

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

3.6 Angles in Polygons

NAME CLASS DATE

3x + 3 4x

6x – 4 5x + 1

BA

CD

Find the indicated measures.

1. 2. 3.

DE � XY � FG �

4. 5. 6.

AB �

FG � AB � WO �

CD � CD �

What special quadrilateral is formed by the shading inside each

triangle? Explain.

7. 8.

45°45°

45°

10

30V G

D

O

B

S

C

W

A

JF G

C D

A B

60

E

A

B

C

D

G

F

y x

D C

F G

BA7

15

GE

X Y

F

38

C

D E

A B16

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

3.7 Midsegments of Triangles and Trapezoids

NAME CLASS DATE

In Exercises 1–4, the endpoints of a segment are given. Determine

the slope and midpoint of the segment.

1. (�1, 1) and (2, 5)

2. (0, �2) and (3, �2)

3. (4, 3) and (4, �5)

4. (�6, 1) and (�3, 0)

In Exercises 5–8, the endpoints of two segments are given. State

whether the segments are parallel, perpendicular, or neither.

5. (2, �4) and (3, 0); (4, �8) and (6, 0)

6. (�3, 1) and (1, 2); (5, 2) and (4, 6)

7. (7, 2) and (0, 6); (�4, 7) and (3, 5)

8. (�4, 0) and (2, 6); (2, 0) and (�1, �3)

Graph quadrilateral ABCD with the given vertices on the grid

provided. Justify the type of quadrilateral it is.

9. A(�2, 3), B(2, 3), C(2, �3), D(�2. �3) 10. D(�1, 5), C(5, 7), A(�1, 0), B(8, 3)

x

y

Ox

y

O

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

3.8 Analyzing Polygons With Coordinates

NAME CLASS DATE

Determine whether the following pairs of figures can be proven to be

congruent. Explain your reasoning.

1. 2. 3.

4. 5. 6.

Suppose that hexagon ABCDEF � UVWXYZ.

7. List all pairs of congruent angles.

8. Name the segment that is congruent to each given segment.

a. b. c.

9. Use the diagram at right to prove that ∆ADC � ∆ADB.

FAXYBC

22

A

C

B

F

E

D

45°

45°

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

4.1 Congruent Polygons

NAME CLASS DATE

CD

B

A

For Exercises 1–10, some triangle measurements are given. Is

there exactly one triangle that can be constructed with those

measurements? If so, identify the postulate that applies.

1. �MNO: MN � 4, m�M � 30°, m�N � 45°

2. �PQR: m�P � 15°, m�Q � 20°, m�R � 145°

3. �LJK: JK � 10, m�J � 12°, m�K � 1°

4. �ABC: AB � 3, BC � 3, m�B � 115°

5. �VWX: VW � 4, WX � 5, m�X � 63°

6. �DBS: DS � 14, m�D � 10°, m�S � 96°

7. �DEF: DE � 3, EF � 4, DF � 3

8. �RST: RS � 13, RT � 10, m�R � 70°

9. �GHI: m�G � 20°, m�H � 40°, m�I � 120°

10. �STU: TU � 5, m�T � 80°, m�U � 80°

Determine whether each pair of triangles can be proven

congruent by using the SSS, SAS, or ASA Congruence

Postulate. If so, identify which postulate is used.

11. 12. 13.

14. Draw a pair of triangles, and write the postulate thatproves them congruent based upon the markings youdrew in your figures.

F

J LKS

R

Q

P

T

M

L O

N

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

4.2 Triangle Congruence

NAME CLASS DATE

For each pair of triangles in Exercises 1–6, is it possible to

prove the triangles congruent? If so, write a congruence

statement and name the postulate or theorem used.

1. 2. 3.

4. 5. 6.

For Exercises 7–9, refer to the diagram at right.

7. �ABE � �CEB by

8. �EDC � �CBE by

9. �EDC � �AEB by

10. Of the three triangles described below, which two are congruent?

�XYZ: m�X � 40°, XY � 9, and m�Y � 30°

�ABC: AB � 9, m�B � 30°, and m�A � 80°

�KLM: m�L � 30°, m�M � 110°, and KL � 9

W X

Y

R

GED

C

B

A

Z

Y

X

N

M

O

J

F G

HD

A

C

B

P

Q

RU

T

S

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

4.3 Analyzing Triangle Congruence

NAME CLASS DATE

A

B

C

E

D

Find each indicated measure.

1. 2. 3.

m�B FG m�Y

4. 5. 6.

XY m�K m�S

Complete the flowchart proof below.

Given: and Prove:

Proof:

Given

Given

8. 9.

7.

MP � NL

�MLP � �NPLML � NP

3x

S

6x

R

Q

70° M

L

K

W 12 Y

X

X Z

Y

40°

H

F

G

15

C

B

A

50°

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

4.4 Using Triangle Congruence

NAME CLASS DATE

L P

M N

MP � NL�MLP � �NPL

ML � NP

�MPL � �NLP

LP � LP

For Exercises 1–10, use a parallelogram labeled as

shown at right. Find each indicated measure.

1. Given MN � 2t and SP � (t + 5), find MN.

2. Given m�M � 45°, m�P � 3x°, and NP � x, find NP.

3. Given m�MSP � 5x° and m�P � x°, find m�MNP.

4. Given m�P � 55°, m�M � (x � 5)°, and NS � (x � 15),find NS.

5. Given m�M � (x � 20)° and m�MNP � (2x � 10)°,find m�M.

6. Given m�MNS � (5x � 10)° and m�NSP � (x � 30)°,find m�MNS.

7. Given MN � 3x, SP � (40 � x), and MS � 2x, find NP.

8. Given m�P � 80°, find m�MNP.

9. Given m�MNP � 120°, m�MSP � 6x°, and NS � (x � 15),find NS.

10. Given MS � 15, NP � (x � 5), and m�P � x°, find m�M.

Explain whether each pair of triangles can fit together to form

a parallelogram without reflecting either triangle.

11. 12. 13.

Z

VQ X

YW

B

F

D

E

C

A

M O

N

R

S T

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

4.5 Proving Quadrilateral Properties

NAME CLASS DATE

S P

NM

For Exercises 1–8, refer to quadrilateral MNOP with diagonals

and intersecting at point Q. For each set of conditions

given, state whether the quadrilateral is a parallelogram. If so,

give the theorem that justifies your answer.

1. and

2. and

3. and

4. and

5. and

6. and

7. and

8. and

Exercises 9–16 refer to parallelogram CLPK with diagonals

and intersecting at point X. For each condition given below,

state whether the parallelogram is a rhombus, a rectangle, or

neither. Give the theorem that justifies your answer.

9. m�K � 90°

10.

11. m�KLC � m�KLP

and m�PCK � m�PCL

12.

13.

14. m�CXL � 90°

15.

16. CK � LP

CK � CL

CL � KP

KL � CP

CL � LP

LK

CP

MP � NOMP � NO

NO � NQMP � NO

MP � POMP � NO

MP � NOMN � PO

NO � POMN � PO

PQ � ONMN � PO

MQ � QOPQ � QN

MN � POMN � PO

NPMO

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

4.6 Conditions for Special Quadrilaterals

NAME CLASS DATE

Construct a figure congruent to each figure below.

1. 2.

3. 4.

Construct the angle bisector of each angle in the triangles below.

Using the intersection of the angle bisectors, construct the

inscribed circle of each triangle.

5. 6. 7.

Construct the perpendicular bisector of each side of the triangles

below. Using the intersection of the perpendicular bisectors,

construct the circumscribed circle of each triangle.

8. 9. 10.

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

4.7 Compass and Straightedge Constructions

NAME CLASS DATE

Translate each figure below by the direction and distance of

the given translation vector.

1. 2. 3.

4. 5. 6.

State whether each triangle described below is possible.

Explain your reasoning.

7. EF � 12, FG � 5, EG � 13

8. SK � 1, KU � 1, SU � 5

9. AL � 104, LD � 53, AD � 51

10. MP � 2.3, PO � 4.6, MO � 5.1

11. QR � , RS � , QS � 1

12. KM � , LM � 5, KL �

13. PQ � , QR � , PR � 93�32�3

�81�64

18

34

12

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

4.8 Constructing Transformations

NAME CLASS DATE

For Exercises 1–12, use the figure and measurements below to

find the indicated perimeter or area. All measurements are in

centimeters.

MS � 15 US � 12

MT � 7 SQ � 20

XP � 13 VO � 10

1. the area of rectangle MNQS

2. the perimeter of rectangle MNQS

3. the area of rectangle MNOU

4. the perimeter of rectangle MNOU 5. the area of rectangle XPQR

6. the perimeter of rectangle XPQR 7. the perimeter of hexagon SRXWVU

8. the area of hexagon SRXWVU 9. the area of ∆PQR

10. If points M and Q were connected by a segment, what would be the area of�MQS?

11. If points M and Q were connected by a segment, what would be the perimeter of �MQS?

12. If points N and W were connected by a segment, what would be the perimeter of �NPW?

the perimeter of trapezoid MNWT?

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

5.1 Perimeter and Area

NAME CLASS DATE

M N

S R Q

UV

O

TX

WP

For Exercises 1–3, find the area of each triangle.

1. 2. 3.

For Exercises 4–6, find the area of each parallelogram.

4. 5. 6.

For Exercises 7–9, find the area of each trapezoid.

7. 8. 9.

Find the area of the indicated figure.

10. �WVZ

11. parallelogram WXYZ

12. trapezoid WXYV

13. right triangle with hypotenuse XY

5

37

10

18 2

6

5

4

11

20

10

26

1

102

6

2 3

8

817

15

6

6

10

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

5.2 Areas of Triangles, Parallelograms, and Trapezoids

NAME CLASS DATE

15

13

16 17

Z Y

XW

V 145

For Exercises 1–10, find the radius of the circle with the given

measurement. Give your answers in terms of π exactly and

rounded to the nearest tenth.

1. A � 36π 2. C � 4π

3. C � 3 4. A � 46

5. A � 212 6. C � 6.2

7. A � 8π 8. 3C � 12π

9. C � 17 10. 2A � 23

11. What happens to the area of a circle when the radius is tripled?

12. What happens to the circumference ofa circle when the radius is quadrupled?

13. If a 10-inch pizza costs $3 and a 12-inch pizza costs $5, which is the better deal? Explain.

14. A solid gold coin with a diameter of 2.9 centimeters sells for $302,and a solid gold coin with diameter 3.1 centimeters sells for $305. Ifboth coins have the same thickness, which is the better deal? Explain.

15. Find the area of the shaded region. The distance from the circle to the center of the shorter base of the trapezoid is 1 unit.

45

12

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.

Practice

5.3 Circumferences and Areas of Circles

NAME CLASS DATE

16

10


For Exercises 1–8, two side lengths of a right triangle are given.

Find the missing side length. Give exact answers.

1. a � 3 b � 7 c �

2. a � 2 b � c � 8

3. a � b � 9 c � 15

4. a � 6 b � c � 12

5. a � b � 1 c � 5

6. a � 12 b � 15 c �

7. a � 13 b � c � 14

8. a � 23 b � 6 c �

Each of the following triples represents the side lengths of a

triangle. Determine whether the triangle is right, acute, or obtuse.

9. 7, 4, 6

10. 8, 42, 47

11. 15, 15, 4

12. 339, 565, 452

13. 14, 52, 49

14. 2, 9, 10

15. What is the length of a diagonal of a square with side lengths of 12?

16. What is the area of an equilateral triangle with side lengths of 4?

c

b

a

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

5.4 The Pythagorean Theorem

NAME CLASS DATE

For Exercises 1–5, refer to �HGF. For each given length, find the

remaining two lengths. Give your answers in simplest radical

form.

1. f �

2. h � 12

3. g � 1

4. g � 5

5. h � 8

For Exercises 6–10, refer to �XVW. For each given length, find

the remaining two lengths. Give your answers in simplest radical

form.

6. x � 3

7. v � 9

8. w � 7

9. v � 14

10. x � 23

In Exercises 11–15, find the area of each figure. Round your

answers to the nearest tenth.

11. 12. 13.

14. a square with a diagonal length of

15. a square with a diagonal length of 5 feet

8�2

3.5

7

4

18 18

18

2�3

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

5.5 Special Triangles and Areas of Regular Polygons

NAME CLASS DATE

f

H g F

h

G

30°

60°

v

W x V

w

X

45°

45°

Find the distance between each pair of points. Round your

answers to the nearest hundredth.

1. (0, 3) and (2, 1) 2. (9, 17) and (4, 5)

3. (�1, 3) and (2, 5) 4. (4, 10) and (6, 13)

5. (7, �3) and (3, 2) 6. (4, �2) and (0, 5)

7. (1, 1) and (4, 7) 8. (3, 8) and (12, 14)

9. (6, 0) and (0, �6) 10. (�7, �11) and (�1, 1)

Graph each set of points. Use the converse of the Pythagorean

Theorem to determine whether the triangle with the given

vertices is a right triangle.

11. (4, 2), (3, �1), and (2, 2) 12. (1, 7), (�3, 3), and (5, 3)

13. (0, 4), (5, 3), and (7, 9) 14. (7, 3), (�2, �2), and (12, �6)

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

5.6 The Distance Formula and the Method of Quadrature

NAME CLASS DATE

Determine the coordinates of the unknown vertex or vertices of

each figure below. Use variables if necessary.

1. isosceles triangle ABC with 2. parallelogram ABCDA(0, 0), B(4, 5), C(?, ?) A(0, 0), B(a, 0), C(? ?), D(b, c), E(?, ?)

3. square STUV 4. trapezoid KLMNS(0, a), T(?, ?), U(?, ?), V(0, �a) K(?, ?), L(a, b), M(?, ?), N(0, 0)

For Exercises 5–13, refer to the diagram of quadrilateral

MNPQ. R, S, T, and U are midpoints.

Find the coordinates of each midpoint.

5. R 6. S

7. T 8. U

Find the slope of each line segment.

9. 10. 11. 12.

13. Using the results from Exercises 5–12, draw a conclusion about

quadrilateral RSTU.

STRUTURS

N M

LK

x

y

V U

TS

x

y

A B

E

D C

x

y

A C

B

x

y

AB � CB

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

5.7 Proofs Using Coordinate Geometry

NAME CLASS DATE

NM R

U

QT P

S

x

y

(0, 0) (2a, 0)

(2b, 2c)

(2d, 2e)

RSTU is a parallelogram.

The slopes of and are equal, so . The slopes of

and are equal, so . Since both pairs of opposite sides are parallel, RSTU is a

parallelogram.

C(a � b, c), E (a � b2

, c2 )

For Exercises 1–6, refer to the spinner at right.

1. What is the probability that the spinner will land on 3?

2. What is the probability that the spinner will land on an even number?

3. What is the probability that the spinner will land on a number less than or equal to 3?

4. What is the probability that the spinner will land on a number larger than 3?

5. What is the probability that the spinner will land on a prime number?

6. Add your results from Exercises 3 and 4. What does this result represent in terms ofprobability?

Find the theoretical probability that a dart tossed at random onto

each figure will land in the shaded area.

7. 8. 9.

10. What is the probability that a randomly generated point with �4 � x � 3 and �6 � y � 1 will lie in a circle centered at (�1, �2) with radius 3?

with radius 1.5?

5

2 3

8

3

52

6

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

5.8 Geometric Probability

NAME CLASS DATE

8 1

2

3

45

6

7

, or 0.512 , or 0.67

1015

For Exercises 1–4, refer to the isometric drawing at right.

Assume that no cubes are hidden from view.

1. Give the volume in cubic units.

2. Give the surface area in cubic units.

3. Draw six orthographic views of the solid in the space at right.Consider the edge with a length of 4 to be the front of the figure.

4. On the isometric dot paper provided below, draw the solid from a different view.

Each of the three solids at right have a volume of 6 cubic units.

5. Draw two other solids with a volume of 6 cubic units that are not just different views of solids A, B, or C.

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

6.1 Solid Shapes

NAME CLASS DATE

Left

A.

B.

C.

For Exercises 1–3, refer to the figure at right.

1. Name a pair of parallel planes.

2. Name two segments skew to .

3. Name two segments perpendicular to plane BFD.

4. In the figure at right, plane M and plane N are parallel.What is the relationship between line p and line q?

5. In the figure at right, line r is perpendicular to line p, but line q is not. If the paper is folded along the line p, which angle will have the measure of the dihedral angle?

For Exercises 6 and 7, indicate whether the statements are

true or false for a figure in space. Explain your answer with

sketches.

6. If line m is in plane P and line n is in plane Q and , thenthe plane P is perpendicular to plane Q.

7. If line p and line q lie in the same plane, and line q and line r liein the same plane, then there is one plane which contains allthree lines.

8. If line r is parallel to line s, and line s and line t are skew, then theplane containing r and s and the plane containing t never intersect.

m � n

BF

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

6.2 Spatial Relationships

NAME CLASS DATE

�

�

p

q

E

p

F

qC

BA

D r

ED

A

B

C

F

For Exercises 1–7, refer to the regular right hexagonal prism at

right.

1. Name the two bases.

2. Name all segments congruent to .

3. How are the two bases related?

4. List all the lateral faces.

5. Name all segments congruent to .

6. What type of quadrilateral is FEKJ?

7. In what manner are the lateral faces related?

In Exercises 8–12, find the length of the diagonal of a right

rectangular prism with the given dimensions.

8. l � 6, w � 9, h � 12

9. l � 4, w � 7, h � 2.3

10. l � a, w � a, h � 2a

11. l � 2a, w � 3a, h � 4a

Find the missing dimensions.

12. l � 10 ft, w � 6 ft, d � 19 ft, h �

13. l � 16 in, h � 21 in, d � 29 in, w �

14. w � 9 cm, h � 8 cm, d � 17 cm, l �

CD

BC

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

6.3 Prisms

NAME CLASS DATE

F E

L M

DG

J K

A B

CH

d

h

w

l

Name the octant, coordinate plane, or axis for each point.

1. (1, �8, 7) 2. (0, 7, 0)

3. (�2, �6, �1.7) 4. (1, 8, �7)

5. (7, 0, 8) 6. (�7, 6, 2)

7. (0, 0, �2) 8. (�2, �3, 4)

For Exercises 9–12, locate each pair of points in a three-

dimensional coordinate system. Find the distance between the

points, and find the midpoint of the segment connecting them.

9. (4, 2, 3) and (8, 5, 5) 10. (8, 3, 5) and (�3, �5, �8)

11. (�3, �1, �5) and (�1, �2, �3) 12. (�6, 3, �7) and (4, �3, 8)

y

x

z

y

x

z

y

x

z

y

x

z

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

6.4 Coordinates in Three Dimensions

NAME CLASS DATE

In the coordinate plane provided, plot the line defined by each

pair of parametric equations.

1. x � 3t 2. x � t � 1y � 1 � t y � t � 1

3. x � 1 4. x � �ty � 2t y � 2

Recall that a trace of a plane is its intersection with the xy-plane.

Find the equation of the trace for each plane defined below.

5. 7x � 4y � 2

6. 3x � 8y � 2z � 8

7. 8x � 4y � 2z � 7

8. �x � 2y � 3z � 10

x

y

x

y

x

y

x

y

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

6.5 Lines and Planes in Space

NAME CLASS DATE

In Exercises 1–4, locate the vanishing point for the figure and

draw the horizon line.

1. 2.

3. 4.

5. In the space below, make a one-point perspective drawing of arectangular solid. Place the vanishing point below the solid.

6. In the space below, make a two-point perspective drawing of arectangular solid. Place the vanishing points below the solid.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

6.6 Perspective Drawing

NAME CLASS DATE

Determine the surface-area-to-volume ratio for a rectangular

prism with the indicated dimensions. Show all of your steps.

1. 2.

3. 4.

5. 6.

Find the surface-area-to-volume ratio for each solid described

below. Show all of your steps.

7. a cube with a surface area of 150 square units

8. a cube with a volume of 512 cubic units

9. a rectangular prism with dimensions

10. a cube with a volume of 8000 cubic units

11. a rectangular prism with dimensions

12. a cube with a volume of 216 cubic inches

13. a rectangular prism with a diagonal length of 19 and a base of 10 � 15

4 � 1 � 1

4 � 4 � 4

25 � 14 � 334 � 16 � 48

7 � 9 � 2224 � 24 � 24

80 � 1 � 14 � 4 � 3

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

7.1 Surface Area and Volume

NAME CLASS DATE

Find the volume of a prism with the given dimensions.

1. 40 in.2, 5 in. 2. 16 m2, 6 m

3. 19 cm2, 84 cm 4. 12 ft2, 8.2 ft

5. 14 cm2, 10 cm 6. 16 ft2, 8 ft

Find the surface area and volume of a right rectangular prism

with the given dimensions.

7. � 14, 2, 15 8. � 3, 6, 2.5

9. � 10, 14, 4 10. � 2.5, 3, 5.5

11. � 6.5, 2.5, 10 12. � 15, 8, 20

13. Find the height of a rectangular prism 14. Find the surface area of a right rectangularwith a surface area of 560 ft2 and a base prism with a height of 6 in. The sides of theof 7 ft � 8 ft. base measure 2 in.

15. A leaning stack of playing cards in the 16. One right prism has triangular bases withshape of an oblique prism has the same base and altitude lengths 12 and 9 ,volume as an upright stack of the same respectively. Another oblique prism hasheight. This is an example of . regular hexagonal bases with side lengths

of 6. If the height of both prisms is 17, do they have equal volumes?

�3

h �w ��h �w ��

h �w ��h �w ��

h �w ��h �w ��

h �B �h �B �

h �B �h �B �

h �B �h �B �

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

7.2 Surface Area and Volume of Prisms

NAME CLASS DATE

Find the surface area of each regular pyramid with side length s

and slant height � given below. The number of sides of the base

is given by n. Round your answers to the nearest tenth, if necessary.

1. 3, 14, � 14 2. 4, 12, � 13

3. 6, 5.2, � 13 4. 3, 1.4, � 19

Find the volume of each rectangular pyramid with height h and

base dimensions � � w. Round your answers to the nearest

tenth, if necessary.

5. 14, � 17.2, 15.8 6. 7, � 3.4, 15

7. 10, � 3.5, 3.5 8. 40, � 16, 5

9. 3, � 5, 6 10. 16, � 8, 2

In Exercises 11–13, find the surface area or the volume of the given

pyramid. Round your answers to the nearest tenth, if necessary.

11. Right triangular pyramid: The side of the equilateral triangular base is 8 cm, the altitude of the pyramid is 12 cm, and its slant height is

cm. Find its surface area.

12. Right rectangular pyramid: The rectangular base is 9 cm � 12 cm, and the altitude of the pyramid is 12 cm. Find its volume.

13. Right square pyramid: The base edges measure 10 cm, the altitude is 12 cm, and its slant height is 13 cm. Find its volume.

14. A pyramid has a right triangle as its base, with leg lengths of 10 cm and 20 cm. If the pyramid’s volume is 600 cm3, find its altitude.

4�10

w ��h �w ��h �

w ��h �w ��h �

w ��h �w ��h �

�s �n ��s �n �

�s �n ��s �n �

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

7.3 Surface Area and Volume of Pyramids

NAME CLASS DATE

For Exercises 1 and 2, find the surface area and volume of each

cylinder.

1. 2.

Find the unknown value for a right cylinder with radius r, height

h, and surface area S. Round your answers to the nearest tenth.

3. 26, 16, 4. 4, 18,

5. , 14, 98 6. 1.6, , 86

7. 0.5, , 4 8. 15, 20,

Find the unknown value for a right cylinder with radius r, height h,

and volume V. Round your answers to the nearest tenth, if necessary.

9. 8, 32, 10. 12, , 144

11. , 16, 80 12. 5.7, 6.5,

13. The limestone pyramid of Khufu weighs about 16 billion pounds. Ifit were reconstructed as a solid cylinder, how large could thecylinder be? Give the largest possible heights, to the nearest ten feet,for diameters of 600 feet, 800 feet, and 1000 feet. Note: limestoneweighs 167 pounds per cubic foot.

?V �h �r �V �h �?r �

V �?h �r �?V �h �r �

?S �h �r �S �?h �r �

S �?h �r �S �h �?r �

?S �h �r �?S �h �r �

5

25

2

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

7.4 Surface Area and Volume of Cylinders

NAME CLASS DATE

In Exercises 1 and 2, find the surface area and volume of each

right cone. Express your answers in terms of π.

1. 2.

Find the surface area of each right cone with radius r, height h,

and slant height �. Express your answers in terms of π.

3. 5.1, 2, � 5.5 4. 13, 17, � 21.4

5. 4.2, 3.8, � 5.7 6. 1.1, 3, � 3.2

Find the volume of each right cone with radius r and height h.

Express your answers in terms of π.

7. 0.5, 4 8. 15, 20

9. 24, 30 10. 8.2, 9

11. The volume of a right cone is 1680π cm3. 12. The surface area of a right cone is 300π cm2.The radius of its base is 12 cm. What is Its slant height and the diameter of its base the height of the cone? are equal. Find its radius.

h �r �h �r �

h �r �h �r �

�h �r ��h �r �

�h �r ��h �r �

4140

9

1512

9

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

7.5 Surface Area and Volume of Cones

NAME CLASS DATE

Find the surface area and volume of each sphere, with radius r or

diameter d. Round your answers to the nearest hundredth.

1. 32 2. 22

3. 3.8 4. 6.2

5. 6 6. 18

In Exercises 7–10, find the surface area and volume of each

sphere with radius r or diameter d. Give exact answers in terms

of π and a variable.

7. 86y 8. 5.2x

9. 10. 2.5y

For Exercises 11–14, consider a sphere with a radius of 16 cm.

11. Find the volume and surface area of the 12. If the radius of the sphere is doubled, whatthe sphere. happens to the surface area?

13. If the radius of the sphere is doubled, 14. If the radius of the sphere is halved, whatwhat happens to the volume? happens to the surface area and volume?

15. If the volume is doubled, how much 16. If the volume is halved, how much shorterlonger is the radius? (Hint: the inverse is the radius?

of the power of 3 is the power of .)13

r �r � (x � 1)

d �r �

d �r �

d �r �

d �r �

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

7.6 Surface Area and Volume of Spheres

NAME CLASS DATE

What are the coordinates of the image when each point below is

reflected across the xy-plane in a three-dimensional coordinate

system?

1. (4, 5, �2) 2. (7, �5, 6)

3. (�1, 5, 6) 4. (4, 3, �2)


reflected across the yz-plane in a three-dimensional coordinate

system?

5. (�14, 6, 8) 6. (8, �6, 0)

7. (�2, 1, �3) 8. (�10, �10, �10)


reflected across the xz-plane in a three-dimensional coordinate

system?

9. (�2, 0, 12) 10. (�7, 3, �9)

11. (�6, �6, 0) 12. (15, 22, �11)

In Exercises 13 and 14, plot the segment with the given endpoints on

the three-dimensional coordinate system provided. Transform each

segment by multiplying each x-coordinate by the given number.

13. A(3, 3, 4) and B(2, �1, 2); 3 14. Q(�3, 4, 1) and R(3, �2, 1); �2

z

y

x

z

y

x

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

7.7 Three-Dimensional Symmetry

NAME CLASS DATE

In Exercises 1–4, the dashed figures represent the preimages of

dilations, and the solid figures represent the images. Find the

scale factor of each dilation.

1. 2.

3. 4.

For Exercises 5–10, given a point and a scale factor, find the line

that passes through the preimage and image, and show that it

contains the origin.

5. (2, 3); 3

6. (1, 4); 2

7. (�1, 2);

8. (3, 4); 1

9. (�4, 3); 2

10.(�3, �3); 1 n � �

n �

n � �

n �13

n � �

n �

y

x

(–3, –1.5)

(2, 1)

y

x

(–2.5, –2)

(5, 4)

y

xO

y

xO

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

8.1 Dilations and Scale Factors

NAME CLASS DATE

In Exercises 1–4, determine whether the polygons are similar.

Explain your reasoning. If the polygons are similar, write a

similarity statement.

1. 2.

3. 4.

Solve each proportion for x.

5. 6.

7. 8.

9. 10.3x � 7

15 �2x � 1

213

x � 3 �5

x � 1

8x �

x50

58

x �

14

16

22x �

218

x18 �

2212

C B

EF

DA

3.0

4.2

1.41.8

1.23.5

M N

XW

YZ

P O

5

6

2

15

E

D F

B

A C20

2412

15

18

16

6

T

8 8

P R

Q

US12

1717

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

8.2 Similar Polygons

NAME CLASS DATE

Yes;�A � �D,�B � �E,�C � �F,and

Determine whether each pair of triangles can be proven similar

by using AA, SSS, or SAS. If so, write a similarity statement, and

identify the postulate or theorem used.

1. 2.

3. 4.

In Exercises 5 and 6, indicate which figures are similar. Explain

your reasoning.

5. 6.

K L

N

P

Q R

O1.5

1.5

2

325°

65°

MJ

912

12

10

7.510

I

F

D

A

G

CH

B

3

5

4

E

2.5

3

1.25

1.5

YX

TW

VU

58°61° 61°

64°

Q

O

N PS R

30°

60°L

K

G

I

H

M1.5

2 2 3

3

F

E

B

A C

D

2.25

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

8.3 Triangle Similarity

NAME CLASS DATE

�ABC � �GHIby SSS because

.

�DEF is not similar

ABGH

�BCDF

�ACGI

� 1.2

because but .

Use the Side-Splitting Theorem to find x.

1. 2.

3. 4.

5. 6.

Name all similar triangles in each figure. State the postulate or

theorem that justifies each similarity.

7. 8. ∠EDA ≅ ∠DAC

B

CA

DE

A

CB

D

AB ⊥ BC, BD ⊥ AC

9

2x + 1

x + 22x + 3

3

x + 1

4 + x

x

x – 2

x – 1

x + 2

x

12

2.57.5

x

12

248

x

10

18

x

5

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

8.4 The Side-Splitting Theorem

NAME CLASS DATE

�EDA � �DAC, so ED �AC.

In Exercises 1–4, use the diagrams to find the height of each

building.

1. 2.

3. 4.

In Exercises 5–8, the triangles are similar. Find x.

5. 6.

7. 8.

5.2

3.9x

43.6 x6

8

6.4

x4.8

9

8

10

6

x

16 ft

24 ft12 ft

24 ft

18 ft

20 ft

45 ft

16 ft

30 ft

40 ft30 ft

36 ft

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

8.5 Indirect Measurement and Additional Similarity Theorems

NAME CLASS DATE

h � 2623

1. In �ABC, D and E are midpoints. What fraction of the area of �ABC is �ADE?

The ratio of the corresponding sides of two similar triangles is .

Find the ratio of the following:

2. their altitudes 3. their perimeters 4. their areas

The side lengths of two squares are 4 cm and 9 cm. Find the ratio

of the following:

5. their diagonals 6. their perimeters 7. their areas

Two spheres have radii of 6 cm and 8 cm. Find the ratio of the

following:

8. the circumferences of 9. their surface areas 10. their volumestheir great circles

The ratio of the base areas of two similar cones is . Find the

ratio of the following:

11. the circumference of 12. their heights 13. their volumestheir bases

14. Two cubes have volumes of 3375 and 1331.What is the ratio of their heights?

15. Suppose that the triangles from Exercise 1 are bases oftwo prisms with the same height. What is the ratio of the volume of the prism with �ADE as a base to the volume of the prism with �ABC as a base?

1625

35

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

8.6 Area and Volume Ratios

NAME CLASS DATE

A

CB

D E

Determine the length of an arc with the given central angle

measure, m�W, in a circle with radius r. Round your answers to

the nearest hundredth.

1. m�W � 20°; r � 1 2. m�W � 26°; r � 18

3. m�W � 70°; r � 24 4. m�W � 110°; r � 6

5. m�W � 45°; r � 4 6. m�W � 10°; r � 5

7. m�W � 15°; r � 7 8. m�W � 25°; r � 6

9. m�W � 25°; r � 12 10. m�W � 14°; r � 13

11. m�W � 53°; r � 7 12. m�W � 123°; r � 18

Determine the degree measure of an arc with the given length, L,

in a circle with radius r. Round your answers to the nearest

hundredth.

13. L � 15; r � 14 14. L � 22; r � 50

15. L � 3; r � 10 16. L � 25; r � 20

17. L � 12; r � 15 18. L � 33; r � 13

19. L � 23; r � 14 20. L � 6; r � 4

21. L � 12; r � 6 22. L � 3; r � 2

23. L � 7; r � 4 24. L � 2; r � 1

For Exercises 25–28, find the degree measure of each arc

by using the central angle measures given in circle F.

25.

26.

27.

28. mBDE�

mEC�

mAEC�

mAB�

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

9.1 Chords and Arcs

NAME CLASS DATE

C

D

B

A

FE

125° 45°

60°110°

Refer to �K, in which at F, for Exercises 1–8.

1.

2. is congruent to which two segments?

3. If KH � 2 and KF � 1, what is MF? What is FH?

4. If KH � 12 and KF � 3, what is MF? What is FH?

5. If KM � 16 and KF � 10, what is MF? 6. If KM � 64 and KF � 20, what is MF?What is FH? What is FH?

7. If KG � 14 and FG � 11, what is MF? 8. If KG � 20 and FG � 12, what is MF?What is MH? What is MH?

9. In the diagram of �O, at E.If CD � 8 and OE � 3, find the length of the radius.

AB�CD

KG

MF �

KG�MH

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

9.2 Tangents to Circles

NAME CLASS DATE

M

H

KF

G

10. In the diagram of �P, the radius is 10,and the distance from the center P to chord

is 6. Find RS.SR

T

P

RS

DC

A

O

B

E

1. �XYZ is inscribed in the circle. If 2. , and are drawn in theand � 100o, circle with center O. If m�AOB � 60°,

find m�Z. find m�ACB.

3. �PQR is inscribed in the circle. If 4. Quadrilateral KLMN is inscribed in the m�P � 70° and � 120°, circle. If � 124° and � 78o,find m�R. find m�KNM.

In �T, m�XTU � 35°, m�VWU � 50°, and

is a diameter. Find the following:

5. m�XWT

6. m�UTV

7. m�WUV

8. m�XTW

9. m

10. m�WTV

11. m�UVT

12. mXU�

WXU�

WU

MK

L

N

RP

Q

mLM�mKL�mPR�

A

C

O

ZY

X

mYZ��Y � �Z

CBOA, OB, CA

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

9.3 Inscribed Angles and Arcs

NAME CLASS DATE

UT

X

W

V

In �L, m � 15°, m � 180°, and m � 50°. is tangent

to �L at H. Find each of the following:

1. m�JHN

2. m�NJH

3. m�JNH

In the figure, is tangent to �S at Q.

4. If m � 105°, find m�RQP.

5. If m�RQP � 110°, find m .

6. If m�RQP � 90°, find m .

7. If m � x � 35, find m�RQP.

8. If m � 2x � 17, find m�RQP.

In the figure at right, and are secants to the circle,

chords and intersect at E, , m � 40°,

and m�ABD � 60°. Find the following:

9. m

10. m�ACD

11. m�AEB

12. m�BDP

13. m�P

AB�

BC�

BA � CDBDAC

PDPA

QP�

QP�

QP�

QP�

QP�QR→

NH←→

HM�

KM�

IK�

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

9.4 Angles Formed by Secants and Tangents

NAME CLASS DATE

NM

H

I

JK L

R

S

PQ

A

P

D

E

B

C

and are tangent to �H, the radius of �H is 4, and ED � 10.

Find the following:

1. EG

2. DH

3. HE

4. FE

5. Name a right angle.

6. Name a pair of complementary angles.

7. Name an angle congruent to �DEH.

8. Name an arc congruent to .

For Exercises 9 and 10, refer to the figure at right. Chords and

intersect inside the circle at E.

9. If AE � 6, EB � 8, and CE � 4, find ED.

10. If AE � 10, EB � 9, and CE � 6, find ED.

For Exercises 11–13, refer to the figure at right. is a tangent

and is a secant to the circle.

11. If PC � 8 and PA � 4, find BA.

12. If BP � 16 and PA � 4, find PC.

13. If BA � 5 and PA � 4, find PC.

PB

PC

CD

AB

DF�

EG←→

ED←→

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

9.5 Segments of Tangents, Secants, and Chords

NAME CLASS DATE

H

F

E

GD

D

A

C

E

B

A

C

P

B

Find the x- and y- intercepts for the graph of each equation.

1. x2 � y 2 � 144 2. x2 � y 2 � 24

3. x2 � y 2 � 25 4. (x � 1)2 � y 2 � 4

5. (x � 5)2 � (y � 5)2 � 25 6. (x � 14)2 � (y � 10)2 � 16

Find the center and radius of each circle.

7. x2 � y 2 � 169 8. x2 � y 2 � 63

9. (x + 12)2 � y 2 � 225 10. (x � 3)2 � y 2 � 81

Write an equation for the circle with the given center and radius.

11. center: (3, 12); radius � 5 12. center: (�2, 6); radius � 7

13. center: (0, 0); radius � 5 14. center: (2, �3); radius � 7

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

9.6 Circles in the Coordinate Plane

NAME CLASS DATE

Find tan A for each triangle below.

1. 2.

3. 4.

5. 6.

For Exercises 7–9, use the definition of tangent ratio to write an

equation involving x. Find the tangent of the given angle with a

calculator, and solve the equation to find the unknown side of the

triangle. Round your answers to the nearest hundredth.

7. 8. 9.

48°

x

17.7

1268°

x

15

41°

x

14

A2.5

1.5 2

A

3√2

A

4

1.84.39

A

3.5

3

1.8

A6

6.462.4

A

6

9 10.82

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

10.1 Tangent Ratios

NAME CLASS DATE

For Exercises 1–10, refer to �ABC.

Find each of the following:

1. sin A

2. sin B

3. cos A

4. cos B

5. tan A

6. tan B

7. m�A

8. m�B

9. (sin A)2 � (cos A)210. (sin B)2 � (cos B)2

For Exercises 11–16, refer to �DEF.

Find each of the following:

11. sin �

12. cos �

13. cos � 14. sin �

15. tan � 16. tan � 2

Use a scientific or graphics calculator for Exercises 17–25. Round

your answers to the nearest hundredth.

17. sin 22° 18. cos 78° 19. tan 12°

20. cos 33° 21. sin 18° 22. tan 2°

23. cos 54° 24. sin 82° 25. tan 76°

12

2

�5

2

�5

1

�5

1

�5

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

10.2 Sines and Cosines

NAME CLASS DATE

A C

B

4

53

D F

E

2

1√5

Use a calculator to find each of the following, rounded to four

decimal places:

1. sin 76° 2. sin 129° 3. sin 307°

4. cos 76° 5. cos 129° 6. cos 307°

7. sin 95° 8. sin 183° 9. sin 359°

10. cos 95° 11. cos 183° 12. cos 359°

13. sin 58° 14. cos 58° 15. sin 32°

In Exercises 16–24, use a calculator to find the sine and cosine of each

angle. Round your answers to four decimal places, and write these values

as x- and y-coordinates of a point at the given angle on the unit circle.

16. 10° 17. 50° 18. 130°

19. 230° 20. 250° 21. 310°

22. 25° 23. 115° 24. 205°

In Exercises 25–36, give two values of angle θ between 0° and 180° for

the given value of sin θ. Round your answers to the nearest degree.

25. 0.9511 26. 0.6691 27. 0.3584

28. 0.5150 29. 0.7880 30. 0.8005

31. 0.2122 32. 0.7194 33. 0.0914

34. 0.2588 35. 0.5878 36. 0.9511

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

10.3 Extending the Trigonometric Ratios

NAME CLASS DATE

In Exercises 1–9, find the indicated measures.

Assume that all angles are acute. It may be helpful to

sketch the triangle roughly to scale. Round your

answers to the nearest tenth.

1. m�A � 48° m�B � 73° b � 1.7 cm a �

2. m�A � 37° m�B � 80° a � 3.4 cm c �

3. m�B � 78° a = 1.45 cm b � 2.63 cm m�A �

4. m�B � 78° a � 1.45 cm b � 2.63 cm c �

5. m�B � 25° m�C � 80° a � 5.2 cm b �

6. m�A � 40° m�B � 64° c � 3.62 cm a �

7. m�A � 41° m�B � 58° a � 14 cm b �

8. m�A � 72° m�B � 40° c � 15 cm a �

9. m�A � 35° a � 8 cm b � 12 cm m�B �

Find all unknown sides and angles for each triangle described

below. If the triangle is ambiguous, give both possible angles.

It may be helpful to sketch the triangle roughly to scale.

10. m�P � 25°, m�Q � 55°, q � 10 11. m�Q � 30°, m�R � 70°, r � 8

12. m�P � 42°, m�R � 34°, q � 9 13. m�R � 48°, p � 3, r � 2.5

14. m�P � 35°, m�R � 41°, q � 23 15. m�Q � 53°, m�R � 72°, p � 26

?

?

?

?

?

?

?

?

?

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

10.4 The Law of Sines

NAME CLASS DATE

A

B

C

a

b

c

Q

P

R

q

p

r

In Exercises 1–5, find the indicated measures.

It may be helpful to sketch the triangle roughly to

scale. Round your answers to the nearest tenth.

1. a � 19 b � 20 c � m�C � 50°

2. a � 8 b � 9 c � 10 m�C �

3. a � 6 b � 6 c � 9 m�B �

4. a � 5 b � 6 c � 8 m�A �

5. a � 3 b � 4 c � m�C �

Solve each triangle.

6. 7.

8. 9.

10. 11.

XZ

z

x

Y

5

22°

25°

A C

B

a

b

45°

2.532°

N

M

n

O3

2

35°

L

J K

j

3

3

55°

I H

G

g

i2.5

39° 41°F

D E3.5

3.92.1

?�33

?

?

?

?

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

10.5 The Law of Cosines

NAME CLASS DATE

A

B

C

a

b

c

Draw the vector sum by using the head-to-tail method.

You may need to translate one of the vectors.

1. 2.

3. 4.

Draw the vector sum by using the parallelogram method.

You may need to translate the vectors.

5. 6.

7. 8.

a

b⇀

⇀

ab⇀

⇀

a⇀

b⇀

a

b

⇀

⇀

a⇀

� b⇀

a

b⇀

⇀

a

b

⇀

⇀

a b⇀⇀

a

b⇀

⇀

a⇀

� b⇀

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

10.6 Vectors in Geometry

NAME CLASS DATE

For Exercises 1–10, a point and an angle of rotation are given. Determine

the coordinates of the image, P�. Round your answers to the nearest tenth.

1. P(0, 2); θ � 30° 2. P(�2, 2); θ � 45°

3. P(3, 4); θ � 180° 4. P(7, 0); θ � 200°

5. P(�3, 2); θ � 12° 6. P(�3, �2); θ � 275°

7. P(5, 3); θ � 38° 8. P(3, �5); θ � 132°

9. P(�2, �4); θ � 10° 10. P(�3, 1); θ � 400°

Find the rotation matrix for each angle of rotation below by filling

in the sine and the cosine values. Round your answers to the

nearest hundredth.

11. 15° 12. 90°

matrix � matrix �

13. 150° 14. 170°


15. 210° 16. 310°


17. 50° 18. 200°


19. 10° 20. 215°

matrix � matrix � � ��

� ��

� ��

� ��

� ��

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

10.7 Rotations in the Coordinate Plane

NAME CLASS DATE

Determine the indicated side length of each golden rectangle.

Round your answers to the nearest hundredth.

1. 2.

3. 4.

5. 6.

7. 8.

9. The golden ratio is equal to the fraction

and approximately equal to the decimal .

?

?

207

?

?

11

13

?

2

?

2?

?

6

?

20

14

?

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

11.1 Golden Connections

NAME CLASS DATE

Find the taxidistance between each pair of points.

1. (2, 4) and (4, 7) 2. (�3, 6) and (5, 4)

3. (�1, �4) and (�3, �6) 4. (100, 82) and (82, 100)

5. (7, �2) and (�6, 4) 6. (�2, 3) and (8, 0)

Find the number of points on the taxicab circle with the given radius.

7. r � 6 8. r � 14

9. r � 21 10. r � 12

Find the circumference of the taxicab circle with the given radius.

11. r � 40 12. r � 13

13. r � 17 14. r � 28

In Exercises 15 and 16, plot the taxicab circle described onto the

grid and find its circumference.

15. center O at (0, 0); radius of 4 units 16. center C at (�2, 3); radius of 5 units

x

y

O

x

y

O

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

11.2 Taxicab Geometry

NAME CLASS DATE

Determine whether the graphs below contain an Euler path, an

Euler circuit, or neither.

1. 2.

3. 4.

5. 6.

7. 8.

C

D

A

B

C D

A

B

A B

CD

EA B C D

A

B C

A B

CD

A

B

C

A

B

C

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

11.3 Graph Theory

NAME CLASS DATE

In Exercises 1–3, determine the number of regions into which the

plane is divided by the curve.

1. 2. 3.

Which of the shapes below are topologically equivalent?

4. 5.

For Exercises 6–9, refer to the simple closed curve

at right.

6. Is point J on the inside or the outside of the curve? Is point M inside or outside?

7. Can you draw a line connecting points J and M thatdoes not intersect the curve? What theorem justifiesyour answer?

8. Into how many regions does the curve divide theplane?

9. Draw a point and connect it to J or M with a line thatdoes not intersect the curve.

A CB

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

11.4 Topology: Twisted Geometry

NAME CLASS DATE

M

J

For Exercises 1–5, refer to the figure that shows line �,

points K and P, and line m on the surface of Poincaré’s

model of hyperbolic geometry.

1. Are perpendicular lines possible in Poincaré’s model?

2. Are rectangles possible in this model?

3. Are lines m and � parallel?

4. How many lines are possible through point K that areparallel to line �?

5. Is there a line through point P that is parallel to line �? If so,how many are possible?

6. Is there a line through point P that is parallel to line m? If so,how many are possible?

For Exercises 7–9, refer to the figure that shows line � on the

surface of a sphere.

7. Are perpendicular lines possible in the spherical geometry?

8. Do two points determine a line in spherical geometry?

9. Given that the radius of the sphere is 1, what is the length ofany line?

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

11.5 Euclid Unparalleled

NAME CLASS DATE

P

Km

�

�

Here are the first two levels in the construction of a fractal.

Level 0: Begin with a line segment.

Level 1: Divide the segment into thirds.Replace the middle third with twosegments whose lengths are each one-third the length of the originalsegment.

1. In the space provided, construct the nextlevel of the fractal by replacing eachsegment of the figure with a one-thirdreplica of level 1.

2. Follow these instructions to create a fractal.

Level 0: Begin with a long strip of paper.

Level 1: Fold the strip’s right end onto its left end, and crease it. Open the strip so that it forms a right angle. Lay the strip on its edge in an L-shape on your desk. Look down at the open strip andsketch this view.

Level 2: Start over. Refold the strip as in Level 1. Now foldthe right end onto the left end a second time. Openthe strip to form right angles. Lay the strip on yourdesk, look down at it, and sketch this view.

Level 3: Start over again. Refold levels 1 and 2. Add level 3by folding again. Open the strip and sketch asbefore.

Level 4: Start over. Refold levels 1, 2, and 3. Add level 4 byfolding again. Open the strip and make the finalsketch.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

11.6 Fractal Geometry

NAME CLASS DATE

Level 1:

Level 2:

Level 3:

Level 4:

For Exercises 1 and 2, sketch the preimage and image for each

affine transformation on the given set of axes.

1. square: O(0, 0); P(�2, 0); 2. triangle: A(2, 2); B(6, 0); C(8, 4)Q(�2, �2); R(0, �2)

T(x, y) � (2x, �2y) T(x, y) �

For Exercises 3–8, use the figure below.

If point P is the center of projection, then

3. the projective rays are .

4. the projection of A onto line �2 is

.

5. the projection of B onto line �2 is

.

If point Q is the center of projection, then

6. the projective rays are .

7. the projection of A onto line �3 is

.

8. the projection of B onto line �3 is .

x

y

O

x

y

(12x, �y)

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

11.7 Other Transformations: Projective Geometry

NAME CLASS DATE

Q

3

1

2

D

C

A

E

F

P

B

�

��

In Exercises 1–6, write a valid conclusion from the given

premises. Identify the form of the argument.

1. If it is a weekend, then José is not at work. It is a weekend.

2. If it is a weekday, then José is at work. José is not at work.

3. If José is not at work, then he is with Anna. José is not with Anna.

4. If José is at work, then he is not with Anna. José is with Anna.

5. If it is a weekday, then José is at work. If José is at work, then he iswearing a tie. It is a weekday.

6. If it is a weekend, then José is not at work. If José is not at work,then he is wearing jeans. It is a weekend.

You are given the following premises:

If you exercise, then you are energized. Jean was energized.Ian exercised. Johan was not energized.Jon did not exercise.

Which of the following conclusions are valid? When possible,

name the argument form.

7. Ian was energized.

8. Jon was energized.

9. Jean had exercised.

10. Johan had exercised.

11. Ian was not energized.

12. Jon was not energized.

13. Jean had not exercised.

14. Johan had not exercised.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

12.1 Truth and Validity in Logical Arguments

NAME CLASS DATE

Write the conjunction of each pair of statements. Determine

whether the conjunction is true or false.

1. A cat is a mammal. France is a country.

2. Butterflies have wings. 3 is an even integer.

Write the disjunction of each pair of statements. Determine

whether the disjunction is true or false.

3. A ray is of finite length. A triangle has 3 sides.

4. Dogs have 4 legs. Birds have 2 legs.

In Exercises 5–12, write the statement expressed by the symbols,

where p, q, r, and s represent the statements shown below.

p: 3 is an odd integer.q: 2 is prime.r: 7 is an even integer.s: 26 is a perfect square.

5. p AND q 6. �(q OR s)

7. �q AND �s 8. q OR �p

9. �p 10. p AND (q OR r)

11. (p AND s) OR �q 12. q OR r Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

12.2 And, Or, and Not in Logical Arguments

NAME CLASS DATE

For each conditional in Exercises 1–3, explain why it is true or

false. Then write the converse, inverse, and contrapositive, and

explain why each is true or false.

1. Conditional: If Aja lives in Texas, she lives in the United States.

Converse:

Inverse:

Contrapositive:

2. Conditional: If 2 � 2 � 3, then 7 � 8 � 56.

Converse:

Inverse:

Contrapositive:

3. Conditional: If an angle lies in the first quadrant, then the sine ofthe angle is positive.

Converse:

Inverse:

Contrapositive:

For Exercises 4–6, write each statement in if-then form.

4. Cindy does not eat meat if she is a vegetarian.

5. 3 is an odd number.

6. I will eat when I am hungry.

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

12.3 A Closer Look at If-Then Statements

NAME CLASS DATE

For Exercises 1–3, determine whether the given argument is an

example of indirect reasoning. Explain why or why not.

1. If Tom joined the army, then his hair was cut short. If his hair was cut short, then it does not cover his ears. But Tom’s hair does cover his ears. Therefore, Tom did not join the army.

2. If I am sleepy, then I yawn. I am yawning. Therefore, I am sleepy.

3. If it were raining, then I would be holding an umbrella. I am not holding an umbrella. Therefore, it is not raining.

Complete the indirect proof below.

In Euclidean geometry, a triangle cannot have two right angles.

Given: �ABCProve: �A and �B cannot both be right angles.

Proof: Suppose that 4. .

It is a property of triangles in Euclidean geometry that the sum of the measures of

the three angles is equal to 5. . Thus m�A � m�B � m�C �

6. . Since �A and �B are 7. ,

8. � 9. � m�C � 10. .

Thus, m�C � 11. . This is a contradiction because

12. . Therefore,

13. .

Co

pyr

igh

t ©

by

Ho

lt, R

ineh

art

and

Win

sto

n. A

ll ri

gh

ts r

eser

ved

.


Practice

12.4 Indirect Proof

NAME CLASS DATE

Use the logic gates below to answer each question.

1. If p � 1 and q � 0, what is the output? 2. If p � 0, q � 1, and s � 0, what is the output?

In Exercises 3–18, complete the input-output table for each

network of logic gates.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

s

qOR

AND

p

q

NOTAND

p

Co

pyrig

ht ©

by H

olt, R

ineh

art and

Win

ston

. All rig

hts reserved

.


Practice

12.5 Computer Logic

NAME CLASS DATE

p q �p p AND q �p OR (p AND q)

1 1

1 0

0 1

0 0

p

q

NOT

ANDORp

p

q NOTNOTAND

p

rOR

ANDq

p q �q p AND �q �(p AND �q)

1 1

1 0

0 1

0 0

p q r q OR r p AND (p OR r)

1 1 1

1 1 0

1 0 1

1 0 0

0 1 1

0 1 0

0 0 1

0 0 0

practice workbook - · pdf filepractice workbook to jump to a location in this book 1. ... 1 0...

Documents