1 Chapter Review

Chapter

1

Chapter Review

Vocabulary Review

acute angle (p. 37) adjacent angles (p. 38) angle (p. 36) angle bisector (p. 46) axiom (p. 18) collinear points (p. 17) compass (p. 44) complementary angles (p. 38) congruent angles (p. 37) congruent segments (p. 31) conjecture (p. 5) construction (p. 44) coordinate (p. 31) coplanar (p. 17)

counterexample (p. 5) foundation drawing (p. 11) inductive reasoning (p. 4) isometric drawing (p. 10) line (p. 17) midpoint (p. 32) net (p. 12) obtuse angle (p. 37) opposite rays (p. 23) orthographic drawing (p. 11) parallel lines (p. 24) parallel planes (p. 24) perpendicular bisector (p. 45) perpendicular lines (p. 45)

plane (p. 17) point (p. 17) postulate (p. 18) ray (p. 23) right angle (p. 37) segment (p. 23) skew lines (p. 24) space (p. 17) straight angle (p. 37) straightedge (p. 44) supplementary angles (p. 38) vertical angles (p. 38)



For: Vocabulary quiz Web Code: auf-0151

Choose the correct term to complete each sentence.

1. Figures that are in the same plane are 9. coplanar

2. A(n) 9 is the part of a line consisting of two endpoints and all points between them. segment

3. Two segments with the same length are 9. congruent

4. A(n) 9 of a segment is a point that divides the segment into two congruent segments. midpoint 5. angle bisector

5. A(n) 9 is a ray that divides an angle into two congruent angles.

6. A conclusion based upon inductive reasoning is sometimes called a(n) 9. conjecture

7. A(n) 9 is an accepted statement of fact. postulate or axiom

8. 9 are coplanar lines that do not intersect. Parallel lines

9. A(n) 9 is an angle whose measure is between 90 and 180. obtuse angle

Skills and Concepts

1-1 Objectives

To use inductive reasoning to make conjectures

16.

You use inductive reasoning when you make conclusions based on patterns you observe. A conjecture describes a conclusion reached using inductive reasoning. A counterexample to a conjecture is an example for which the conjecture is incorrect.

Find a pattern for each sequence. Describe the pattern and use it to show the next two terms. 10?15. See margin.

10. 40, 35, 30, 25, c

11. 5, ?5, 5, ?5, c

12. 34, 27, 20, 13, 6, c

13. 6, 24, 96, 384, c

14. 2, 4, 8, 16, 32, c

15. 1, 2, 5, 6, 9, c

16. Draw the next figure in the sequence. See left.

Chapter 1 Chapter Review 71

10. subtract 5; 20, 15

11. Answers may vary. Sample: mult. by ?1; 5, ?5

12. subtr.7; ?1, ?8

13. mult. by 4; 1536, 6144

14. mult. by 2; 64, 128

15. alternate adding 1 and 3; 10, 13

1 Chapter Review

Resources

Student Edition Extra Skills, Word Problems, Proof

Practice, Ch. 7, p. 728 English/Spanish Glossary, p. 779 Postulates and Theorems, p. 770 Table of Symbols, p. 763

Vocabulary and Study Skills worksheet 1D

Spanish Vocabulary and Study Skills worksheet 1D

Interactive Textbook Audio Glossary

Online Vocabulary Quiz

Spanish Vocabulary/Study Skills ELL

VNamoe cabulary/StudyClass Skills Date

L3

1D: Vocabulary

For use with Chapter Review

Study Skill: Many words in English have more than one meaning. Often a word has one meaning in ordinary conversation, and a different specific meaning or exact definition when it is used in math or science or grammar. You can often figure out which meaning to use by looking at the sentence that contains the word. To help you decide what a word means, consider the surroundings, or context, in which you see the word.

Read the mathematical definition in the left column and the sentence in the right column. In the blank in the middle, write the one word from the list below that fits both the definition and the sentence. The first one is done for you.

base natural real

like power term

origin element

constant open

Definition

Sentence

1. kind of number in a set of rational and irrational numbers together

2. a term that has no variable

3. a number that is multiplied repeatedly

real

It is a

event.

It actually happened.

That noise is

.

It just never seems to stop.

Put this statue on its so it will not fall over.

4. the kind of terms that have exactly the same variable factors

5. the kind of math sentence that has one or more variables

6. the base and exponent of an expression of the form an

7. the kind of number you might use to count rocks or pencils

8. the point where the axes of a coordinate plane intersect

9. a number, a variable, or the product of a number and one or more variables

I really

that kind

of food. It is my favorite.

The door should be so the customers can come in.

Turn off the before you try to repair those

wires.

Let's go for a walk by the lake. I want to enjoy the

world.

What is the

of

that custom? I wonder how it

began.

He will come home from college at the end of the

.

10. the name of each item in a matrix

One

in water is

oxygen. The other is hydrogen.

4

Reading and Math Literacy Masters

Algebra 1

? Pearson Education, Inc. All rights reserved.

71

18.

3 1265

4

1-2 Objectives

To make isometric and orthographic drawings

To draw nets for threedimensional figures

A net is a two-dimensional pattern that you can fold to form a three-dimensional figure. A net shows all surfaces of a figure in one view.

17. The net at the right is for a number cube. What are the

three sums of the numbers on opposite surfaces of the

5

cube? 4, 6, 11

1234

18. On another number cube, the numbers on each pair of

opposite surfaces add to 7. Draw a net for this number

6

cube. See margin.

1-3 and 1-4 Objectives

To understand basic terms and postulates of geometry To identify segments and rays To recognize parallel lines

21. AQTD and BRSC

23. always

Points that lie on the same line are collinear points. Points and lines in the same plane are coplanar. Segments and rays are parts of lines.

Lines that are coplanar and do not intersect are parallel lines. Lines in space that are not parallel and do not intersect are skew. Planes that do not intersect are parallel planes.

Use the figure at the right for Exercises 19?22.

4

4

19. Name two intersecting lines. AQ and QR

19?22. Answers may vary.

Samples are given.

T

S

20. Name three noncollinear points. A, Q, R

21. Name a pair of parallel planes.

Q D

R C

22. N4ame4thre4e lines that intersect at D. AD,TD,CD

A

B

Complete with always, sometimes, or never to make a true statement. sometimes

23. A line and a point are 9 coplanar. 24. Two segments are 9 coplanar.

25. Skew lines are 9 coplanar. never 26. Two points are 9 collinear. always

1-5 and 1-6 Objectives

To find the lengths of segments

To find the measures of angles

To identify special angle pairs

Segments with the same length are congruent segments. A midpoint of a segment divides the segment into two congruent segments.

Two rays with the same endpoint form an angle. Angles can be classified as acute, right, obtuse, or straight. Angles with the same measure are congruent angles.

27. Find two possible coordinates of Q so that PQ = 5. ?7, 3

28. Find the coordinate of the midpoint of PH. 0.5

P

H

4 3 2 1 0 1 2 3 4

x2 Algebra Find the value of each variable.

29. 3m + 5 4m - 10 15

A

B

C

30. (3x 31) (2x 6) 31

31. Answers may vary.

Samples are given. a. /ADB, /BDC b. /ADE, /EDF c. /ADC, /EDF

31. Name a pair of each of the following. a. complementary angles b. supplementary angles c. vertical angles

AB C

D

E

F

72 Chapter 1 Chapter Review

72

1-7 Objectives

To use a compass and a straightedge to construct congruent segments and congruent angles

To use a compass and a straightedge to bisect segments and angles

Construction is the process of making geometric figures using a compass and a straightedge. Four basic constructions involve constructing congruent segments, congruent angles, and bisectors of segments and angles.

Perpendicular lines intersect at right angles. A perpendicular bisector of a segment is perpendicular to the segment at its midpoint, and bisects it into two congruent segments. An angle bisector is a ray that divides an angle into two congruent angles.

32. Use a protractor to draw a 648 angle. Then construct an angle congruent to your 648 angle. See margin.

33. Use a ruler and draw PQ.

a. Construct AB > PQ. a?b. See margin.

P

Q

b. Construct the perpendicular bisector of AB.

AltNeamre native AssessmClassent

Alternative Assessment

Chapter 1

Use a straightedge and compass for all four tasks. TASK 1

a. Explain in detail the patterns you observe in Figures 1, 2, and 3. b. Given those patterns, draw Figure 4. Is there more than one possible

answer for Figure 4? Explain. c. What would Figure 5 look like? Describe.

Date

L4

Form C

??

Figure 1

Figure 2

Figure 3

Figure 4

TASK 2

a. Draw and label a figure that fit*s th)e foll*owi)ng* de) scription: * )

Plane P contains parallel lines AB and EG . CD intersects AB at point B, but C and D are not in plane P. Angles ABG, CBA, and DBA are three different right angles.

b. Can you name three noncoplanar points in your figure? Explain.

c. Name three points that are not collinear.

? Pearson Education, Inc. All rights reserved.

1-8 Objectives

To find the distance between two points in the coordinate plane

To find the coordinates of the midpoint of a segment in the coordinate plane

The x-axis and the y-axis intersect at the origin (0, 0) and determine a coordinate

plane. You can find the coordinates of the midpoint M of AB with endpoints

A(x1, y1) and B(x2, y2) using the Midpoint Formula.

M = ax1

1 2

x2 , y1

1 2

y2 b

You can find the distance d between points A(x1, y1) and B(x2, y2) using the Distance Formula.

d = #Ax2 2 x1B2 1 Ay2 2 y1B2

Find the distance between the points to the nearest tenth.

34. A(-1, 5), B(0, 4) 1.4 units

35. C(-1, -1), D(6, 2) 7.6 units

GH has endpoints G(?3, 2) and H(3, ?2).

36. E(-7, 0), F(5, 8) 14.4 units

37. Find the coordinates of the midpoint of GH. (0, 0)

38. Find GH to the nearest tenth. 7.2 units

Geometry Chapter 1

32.

64

33. a ? b.

Form C Test

31

The perimeter P of a polygon is the sum of the lengths of its sides. The area A of a

1-9 Objectives

polygon is the number of square units it encloses.

A

B

To find perimeters of rectangles and squares,

Formulas:

Square

Rectangle

Circle

and circumferences of circles

To find areas of

P = 4s A = s2

P = 2b + 2h A = bh

C = pd or C = 2pr A = pr2

rectangles, squares, and circles

Find the perimeter and the area of each figure.

39.

40.

8 cm

41. 6 ft

P 32 cm A 64 cm2

13 ft

P 38 ft A 78 ft2

3 in. 5 in. P 32 in.

A 40 in.2

Find the circumference and the area of each circle to the nearest hundredth.

42. r = 3 in. C N 18.85 in. A N 28.27 in.2

43. d = 15 m C N 47.12 m, A N 176.71 m2

44. r = 26 m C N 163.36 m, A N 2123.72 m2

Chapter 1 Chapter Review 73

73

1 Chapter Test

Chapter

1

Chapter Test



For: Chapter Test Web Code: aua-0152

? L3 Ch. 1 Test ? L2 Adapted Ch. 1 Test ? L4 Ch. 1 Alternative

Assessment ? L3 Spanish Ch. 1 Test ? L4 Spanish Ch. 1 Alternative

Assessment ? L2 Informal Geometry Ch. 1

Test, Forms D & E ? ExamView CD-ROM

? Ch. 1 Pre-Made Test ? Make your own Ch. 1 test ? Online Chapter 1 Test at

Adapted Chapter Test

ChaNapme ter Test

Class

Chapter Test

Chapter 1

Describe each pattern, and find the next two terms or drawings in each sequence.

1. 12, 17, 22, 27, . . .

2.

-1,

1 2

,

-41

,

1 8

,

.

.

.

4.

L2

Date

L3

Form A

3. 7, 11, 16, 22, . . .

? Pearson Education, Inc. All rights reserved.

5. Critical Thinking Make a conjecture about the relationship between

three consecutive whole numbers based on this relationship illustrated by the numbers 3, 4, and 5: (3 5) = 42 - 1. Can you find a

counterexample? A

Use the figure to answer Exercises 6?9.

6. Name three collinear points. 7. Name four coplanar points. 8. Name four noncoplanar points.

G

E

O

9. Find* ea) ch intersection. a. C* D) and plane P b. E* F)and *plan) e P

c. AB and CD d. plane P and point G

C B

Use the figure to answer Exercises 10?13.

*)

10. Name a line parallel to BC.

*)

11. Name two lines skew to DF.

12. Name a pair of parallel planes.

E B

D

A

F

C

13. Name two intersecting planes.

14. Algebra MP = 62. Use the figure to find each of the following.

a. x b. MR c. RP

2x

3x 7

M

R

P

15. Error Analysis Show that the conjecture below is false by finding a counterexample.

If two lines do not intersect, then they are not coplanar lines.

D P

F

Geometry Chapter 1

Form A Test

27

Describe each pattern and find the next two terms of each sequence. 1?3. See margin.

1. 8, -4, 2, -1, c

2. 0, 2, 4, 6, 8, c

3.

S

R

Q

P

4. Open-Ended Write two different sequences whose first three terms are 1, 2, 4. Describe each pattern. See margin.

5. Draw a net for a cube. See margin.

Use the figure for Exercises 6?9.

A EB Q D

C

6. Name three collinear points. A, B, C

7. Name four coplanar points.*

Sample: A, B, C, D

)

8. What is the intersection of AC and plane Q? B

x2 16. Algebra JK = 48. Find the value of x. 10

J

H

K

4x 15

2x 3

x2 17. Algebra M(x, y) is the midpoint of CD with endpoints C(5, 9) and D(17, 29). a. Find the values of x and y. (11, 19) b. Show MC = MD. MC MD "136

18. To the nearest tenth, find the perimeter of nABC with vertices A(-2, -2), B(0, 5), and C(3, -1). 19.1 units

For the given dimensions, find the area of each figure to the nearest hundredth.

19. rectangle

20. square

21. circle

b = 4m

s = 3.5 in.

h = 2 cm

12.25 in.2

800 cm2 or 0.08 m2

d = 9 cm 63.62 cm2

x2 Algebra Use the figure for Exercises 22?24. In Exercises 22 and 23, find the value of each variable.

B

K

J

9. Ho* w m) any planes contain eac* h li)ne and each point? a. *BD) and point A 1 b. *AB) and point C

c. BE and point C 1 d. BD and point E 1 9b. infinitely many

10. Track The running track is a rectangle with a half circle on each end. If FI and GH are diameters, find the area inside the track to the nearest tenth. F 212 ft G 29,054.0 ft2

100 ft

I

H

Complete with always, sometimes, or never to make

each st)atement) true.

11. LJ and TJ are 9 opposite rays. never

12. Four points are 9 coplanar. sometimes

13. Skew lines are 9 coplanar. never

14. Two segments that lie in parallel lines are 9 parallel. always

15. The intersection of two planes is 9 a point. never

D

R

22. m&BDK = 3x + 4, m&JDR = 5x - 10 7

23. m&BDJ = 7y + 2, m&JDR = 2y + 7 9

24. Name two complementary angles. Answers may vary. Sample: &BDJ, &JDR

25. Writing Why is it useful to have more than one way of naming an angle? See margin, p. 75.

26. Draw an obtuse &ABC. Use a compass and straightedge to bisect the angle. See margin, p. 75.

Use the figure to complete Exercises 27?30.

27. VW is the 9 of AY. # bisector V

28. If EY = 3.5, then AY = 9. 7

29.

1 2

9

=

AE

AY

30. 9 is the midpoint of 9. A

E W

Y

E; AY

31. Carpeting How many square yards of carpet are

needed to carpet a room that is 15 ft long and

20 ft wide?

33

1 3

yd2

74 Chapter 1 Chapter Test

Chapter Test 1. Div. each preceding term by ?2; 12, ?14 2. Add 2 to the preceding term; 10, 12

74

3. Rotate the U clockwise one-quarter turn. Alphabet is backwards;

ON

4. Answers may vary. Sample:

1, 2, 4, 8, 16, 32, . . .

5.

1, 2, 4, 7, 11, 16, . . .

In the first seq. double

each term. In the second

seq., add consecutive

counting numbers.

READING COMPREHENSION

Standardized Test Prep

Standardized Test Prep

Reading Comprehension Read the passage below, then answer the

questions on the basis of what is stated or implied in the passage.

Instructions for Building the Rainbow Toy Chest

Use 34-in.-thick plywood. ? Cut the top and bottom 18 in. by 42 in.

Paint the top red and the bottom violet. Use 12-in.-thick plywood. ? Cut the two sides 18 in. by 60 in.

Paint: left side brown, right side white. ? Cut the three shelves 15 in. by 41 in.

Paint: top orange, middle yellow, bottom green. ? Cut the two dividers 24 in. by 15 in.

Paint: left blue, right indigo.

Use particleboard. ? Cut the back 41 in. by 60 in. Paint the back gray.

Assemble the painted pieces using nails and glue.

Students must be able to extract information from reading passages, answer multiple-choice questions, and construct responses in order to be successful on current state and national assessments.

To answer the questions, students apply skills and concepts from this chapter and previous chapters. Multiple Choice: Items 1?8 Free Response: Items 9?12

Resources

Test Prep Workbook Grab & Go ? L3 Cumulative Review ExamView CD-ROM ? Standardized Test Practice

1. How many pieces must be cut to make the

D chest?

5

7

9

10

2. What is the shape of each piece?

G

square

rectangular

round

cannot be determined

3. Which uses thicker wood, a divider or the top?

B

divider

top

same thickness cannot be determined

Assume that the toy chest has been assembled.

4. Take the top of the bookshelf as the first H horizontal surface and count downward. What is

the color of the fourth surface down?

white

yellow

green

blue

5. Which corners are NOT coplanar?

B

the four corners of the right side

the two top corners of the left side and the

two front corners of the bottom

the two top corners of the right side and

the two bottom corners of the left side

the two front corners of the top and the

two back corners of the bottom

25. Answers may vary. Sample: Some ways of naming an l can help identify a side or vertex.

26.

A

6. Where do the violet board and the J particleboard meet?

the front edge of the violet board the back edge of the left side the right edge of the bottom the bottom edge of the back

7. Which edge is skew to the front edge of the B orange board?

the left edge of the orange board the top edge of the white board the back edge of the yellow board the front edge of the middle shelf

8. What are the colors of two boards that are NOT H perpendicular?

blue and gray blue and white

indigo and violet yellow and brown

9. How tall is the toy chest? 6121 in. 10. What is the area of the top? 756 in.2

11. What is the perimeter of the front? 207 in.

12. The back edge of each shelf touches the back of

the chest. How far "recessed" is the front edge

of a shelf from the front edge of a side?

2

1 4

in.

Chapter 1 Standardized Test Prep 75

? Pearson Education, Inc. All rights reserved.

Spanish Assessment Resources ? L3 Spanish Cumulative Review

Spanish Cumulative Review

ELL

CumNameulative ReviewClass

Date

L3

Cumulative Review

Chapter 1

For Exercises 1?13, choose the correct letter.

1. Find a pattern for the sequence. Use the pattern to show the next term.

1, 3, 9, 27, c

A. 81

B. 45

C. 41

D. 36

2. If XY = 12, what is the measure of XZ?

X

2x 2 Y

3x 1

A. 35

B. 26

3. If EG = 42, find the value of y.

Z C. 24

D. 14

E

3y 4

F

5y 2

G

A. 5

B.

5

1 2

C. 6

D. 7

4. Find a pattern for the sequence. Use the pattern to show the next term.

S, M, T, W, c

A. S

B. H

C. M

D. T

Use the figure at the right for Exercises 5?8.

5. Wh*at is) the intersection of plane GHIJ and* pl)ane CDIH?

*)

A. GH

B. point H

C. CD

D. HI

6. Which four points are coplanar?

A. A, B, E, I

B. B, C, D, E

C. A, C, F, H

D. E, F, I, K

7. What is another way to* na)me plane ABEF?

A. point A

B. CD

C. plane ACDF

* )

8. What is the intersection of BE and plane A* CH) G?

A. BC

B. point E

C. BK

D. plane CDIH D. point B

C B A

H G

DK FE

I J

9. Find the value of x. A. 3 B. 4 C. 5

D. 10

Q (4x 5)? (8x)?

R

)

10. OM is the 9 of &LON. A. perpendicular bisector C. segment bisector

ST

B. midpoint D. angle bisector

O N

M L

Geometry Chapter 1

Cumulative Review

33

B

C

75

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download