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