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Geom_3eTE.03EM.X_189-193 3/24/06 11:13 AM Page 189
Chapter
3
Chapter Review
3
Chapter Review
Vocabulary Review
Resources
equilateral polygon (p. 160)
exterior angle of a polygon (p. 149)
flow proof (p. 135)
isosceles triangle (p. 148)
obtuse triangle (p. 148)
point-slope form (p. 168)
polygon (p. 157)
regular polygon (p. 160)
remote interior angles (p. 149)
acute triangle (p. 148)
alternate exterior angles (p. 129)
alternate interior angles (p. 127)
concave polygon (p. 158)
convex polygon (p. 158)
corresponding angles (p. 127)
equiangular triangle (p. 148)
equiangular polygon (p. 160)
equilateral triangle (p. 148)
right triangle (p. 148)
same-side exterior angles (p. 129)
same-side interior angles (p. 127)
scalene triangle (p. 148)
slope-intercept form (p. 166)
standard form of a
linear equation (p. 167)
transversal (p. 127)
two-column proof (p. 129)
Student Edition
Extra Skills, Word Problems, Proof
Practice, Ch. 3, p. 720
English/Spanish Glossary, p. 779
Postulates and Theorems, p. 770
Table of Symbols, p. 763
Vocabulary and Study Skills
worksheet 3F
Spanish Vocabulary and Study
Skills worksheet 3F
Interactive Textbook Audio
Glossary
Online Vocabulary Quiz
Choose the correct vocabulary term to complete each sentence.
1. In a triangle, an angle is right, obtuse, or 9. acute
2. A(n) 9 angle has a measure between 90 and 180. obtuse
3. When two coplanar lines are cut by a transversal, two angles that are in similar
positions on the same side of the transversal are called 9. corresponding
angles
4. The measure of a(n) 9 angle of a triangle is equal to the sum of the measures
of its two remote interior angles. exterior
5. A polygon is 9 if no diagonal contains points outside the polygon. convex
6. A(n) 9 polygon has all angles congruent. equiangular
7. A(n) 9 polygon is both equiangular and equilateral. regular
PHSchool.com
For: Vocabulary quiz
Web Code: auj-0351
8. The linear equation y - 3 = 4(x + 5) is written in 9 form. point-slope
9. From the 9 form of a linear equation, you can easily read the value of the
slope and the value of the y-intercept. slope-intercept
10. When two coplanar lines are cut by a transversal, the angles between the two
lines and on opposite sides of the transversal are called 9.
alternate interior angles
Spanish Vocabulary/Study Skills
Skills and Concepts
Vocabulary/Study Skills
Name
Class
3D: Vocabulary
To identify angles
formed by two lines and
a transversal
To prove and use
properties of parallel
lines
t
A transversal is a line that intersects two
coplanar lines at two distinct points.
&1 and &4 are corresponding angles.
&3 and &4 are alternate interior angles.
&2 and &4 are same-side interior angles.
Study Skill: You will encounter many new terms as you read a mathematics
textbook. Read aloud or recite the new terms as you read them. This will
help you remember and recall rules, definitions and formulas for future use.
It is important to learn the definitions of new terms as soon as they are
introduced and continue to increase your vocabulary.
ᐉ
1
2
L3
Date
For use with Chapter Review
Unscramble the UPPERCASE letters to form a math word or phrase that
completes each sentence. Copy the letters in the numbered cells to the cells
with the same number at the bottom of the page.
3
1. COOPDUNM EUNIISAQELTI are joined by and or or.
4
k
6
16
13
2. An TEITINYD is an equation that is true for every value.
19 20 3
3. The NRGEA of a set of data is the difference between the greatest and least data values.
5
If two parallel lines are cut by a transversal, then
4. A data value that is much higher or lower than the other data in a set is an LEUTORI.
9
5. An XENNPTEO shows repeated multiplication.
• corresponding angles are congruent.
28
15
14
6. A coordinate plane is divided by its axes into four TANQAUSRD.
• alternate interior angles are congruent.
2
23 25
7. You IMPIYSLF an equation when you replace it with its simplest name or form.
32
1
© Pearson Education, Inc. All rights reserved.
3-1 Objectives
ELL
22
8. A EVBALRAI is a symbol, usually a letter, which represents one or more numbers.
• same-side interior angles are supplementary.
12
18
9. The numerical factor when a term has a variable is a CINCEFFITOE.
11. Suppose / and k in the diagram above are parallel. If m&1 = 59, what are the
measures of &2, &3, and &4? ml2 121, ml3 59, ml4 59
26 21 31
4
8
17
11
11. The multiplicative inverse of a number is always its RLREIPACCO.
30
1
Chapter 3 Chapter Review
10 27 24 29
10. LOHWE SURBEMN are the nonnegative integers.
189
2
3
7
4
5
6
7
8
9 10 11
12 13
14 4 15
16 17 18 19 20
21 22
23 4 24
25 26 27 28 29 30 31 32
12
Reading and Math Literacy Masters
Algebra 1
189
Geom_3eTE.03EM.X_189-193 3/24/06 11:13 AM Page 190
13. ml1 75; same side
int. ' are suppl.
ml2 105; alt. int. '
are O or two ' that form
a straight l are suppl.
14. ml1 55; same side
int. ' are suppl. ml2 90; alt. int. ' are O.
Find m&1 and then m&2. Justify each answer. 13–14. See margin.
12. ml1 120; corr. '
are O. ml2 120;
vert. ' are O or alt.
ext. ' are O.
12.
2
1
3-2 and 3-8 Objectives
To recognize conditions
that result in parallel
lines
a
To construct parallel
lines
To construct
perpendicular lines
a
r
13. q
21
b
c
19.
a
p
120
y
You can construct the line parallel to a given line through a given point not on the
line. You can also construct the perpendicular to a given line at a given point on the
line or through a given point not on the line.
x 2 Algebra Find the value of x for which < n m.
ᐉ
18.
m
16.
20
130
ᐉ
(2x 10)
m
17. ᐉ
24
(3x 20)
m
(5x 32)
Use the segments at the right for Exercises 18 and 19.
b
3-3 Objective
To relate parallel and
perpendicular lines
20. If 2 lines are ' to the
same line, then the lines
are n (Thm. 3-10).
3-4 Objectives
To classify triangles and
find the measures of
their angles
To relate exterior angles
to the angles of a
triangle
a
18. Construct a rectangle with side lengths a and b.
See left.
19. Construct a quadrilateral with one pair of parallel
opposite sides, each side of length 2a. See margin.
b
If two lines are perpendicular to the same line, then the two lines are parallel. If a
line is perpendicular to one of two parallel lines, then it is perpendicular to both
lines. Both of these statements are true only if the lines are coplanar.
Use the diagram at the right for Exercises 20 and 21.
State the theorem that justifies each statement.
a
b
c
20. If b ' c and b ' d, then c 6 d.
d
21. If c 6 d, then a ' c.
If a line is ' to one of two n lines, then it is
also ' to the other (Thm. 3-11).
The sum of the measures of the angles of a triangle is 180. The measure of each
exterior angle of a triangle equals the sum of the measures of its two remote
interior angles.
Find the values of the variables. Then classify each triangle by its sides and angles.
x 45; y 45;
x 60; y 60; equilateral,
22.
23.
24.
isosc., right
acute
x
x
60
8
5
78
41
7
61; scalene, acute
190
1
2
105
w
65
(3x 5)
190
x
125
Two lines cut by a transversal are parallel if corresponding angles are congruent,
alternate interior angles are congruent, or same-side interior angles are
supplementary.
15.
20
a
14. z
Chapter 3 Chapter Review
x
y 120
y
135
Geom_3eTE.03EM.X_189-193 3/24/06 11:13 AM Page 191
Alternative Assessment
Name
In each of Exercises 25–28, the measures of the three angles of a triangle are given.
Find the value of x and then classify the triangle by its angles.
Class
L4
Date
Alternative Assessment
Form C
Chapter 3
TASK 1
25. x + 10, x - 20, x + 25 55; acute
a. Finish labeling the figure, given the following: lines a and b are cut by
transversal t; ⬔3 and ⬔8 are same-side interior angles; ⬔4 and ⬔6 are
corresponding angles, as are ⬔7 and ⬔3; and ⬔5 and ⬔3 are alternate
interior angles.
26. x, 2x, 3x 30; right
1 2
4 3
b. Name three different conditions, each involving ⬔8 and another angle,
any one of which is sufficient to guarantee that a 6 b.
27. 20x + 10, 30x - 2, 7x + 1 3; acute
28. 10x - 3, 14x - 20, x + 3
8; obtuse
29. In a right triangle, what is always true about the angles?
One l is 90; the remaining 2 ' are comp.
c. If a 6 b and m⬔1 = 105, give the measure of the other seven angles.
d. Write a flow proof for the following statement: If ⬔7 and ⬔4 are
supplementary, then a 6 b.
TASK 2
* )
* ) * )
* ) * )
© Pearson Education, Inc. All rights reserved.
Draw AB . Construct PB # AB . Then construct PQ 6 AB .
A polygon is a closed plane figure with at least three sides. To name a polygon, start
at any vertex and list the vertices consecutively in a clockwise or counterclockwise
direction. A polygon is convex if no diagonal contains points outside the polygon.
Otherwise, it is concave.
3-5 Objectives
To classify polygons
To find the sums of the
measures of the interior
and exterior angles of
polygons
An equilateral polygon has all sides congruent. An equiangular polygon has all
angles congruent. A regular polygon is equilateral and equiangular.
Geometry Chapter 3
31
Form C Test
The sum of the measures of the angles of an n-gon is (n - 2)180. The sum of the
measures of the exterior angles of an n-gon, one at each vertex, is 360.
Find the measure of an interior angle and an exterior angle of each
regular polygon.
30. a hexagon
31. an octagon
32. a decagon
33. a 24-gon
120; 60
135; 45
144; 36
165; 15
34. What is the sum of the measures of the exterior angles for each polygon in
Exercises 30–33? 360
When a linear equation is in slope-intercept form, y = mx + b, the slope m and
the y-intercept b are easily identified. When a linear equation is in point-slope form,
(y - y1) = m(x - x1), point (x1, y1) and slope m can easily be identified. The
equation Ax + By = C, where A and B are not both zero, is in standard form.
When a linear equation is in standard form, the x- and y-intercepts are readily found.
35–38.
35. Name the slope and y-intercept of y = 2x - 1. Graph the line. See margin.
3-6 Objectives
To graph lines given
their equations
To write equations of
lines
36. Name a point on and the slope of y - 3 = -2(x + 5). Graph the line.
Spanish Quarter 1 Test - Forms A, B ELL
Name
37. Graph y = 2 12.
38. Graph 3x - 4y = 12.
39. Write an equation for the vertical line that contains A(6, -9). x 6
Class
Date
Chapter Test
Form A
Quarter 1 Test - Forms D, E
Chapter 6
Quarter 1 Test — Forms A, B
Graph quadrilateral ABCD. Then determine the most precise name for
Name
Class
each quadrilateral.
1. A(2, 3), B(-4, 3), C(-2, 6), D(1, 6)
2. A(1, 2), B(3, 8), C(5, 2), D(3, -4)
Quarter
1 Test
3. A(-1, 4), B(2, 4), C(2, 0), D(-1, 0)
L2
L3
Date
4. A(0, 6), B(3, 3), C(0, -5), D(-3, 3)
Form A
Chapters 1–3
Find QV in each parallelogram.
1. Find the next two terms in the sequence.
Q 8, …
V
5. 1, 2, 3, 5,
6. Q
4 cm a counterexample for the following
2. Provide
statement:
If the
T animal has four legs,
U then it is a dog.
The slopes of two nonvertical parallel lines are equal. All vertical lines are parallel.
3-7 Objectives
10. Create an isometric drawing from the
R foundation drawing.
7. Q
T
5 cm
* )
All rights reserved.
8.
43. A(-1, 3), B(4, 8), C(-6, 0), D(2, 8) n
42. A(-3, 3), B(0, 2), C(1, 3), D(-2, -6)
#
* )
44. Writing For B(4, 8) and D(2, 8), find the slope of BD . Explain why the slope of
any horizontal line is zero. 0; the difference of y-coordinates is always zero.
Chapter 3 Chapter Review
SFront
X
36. m 2;
point (5, 3)
y
3
1
O
3
1
x
y
37.
1
(4x 40)
38
(3x)
10. AC = 7x - 15, BD = 4x + 15
y
A
2
1
4
2 O x
O
1
1x
B
1
(2x)
4. Draw a net for the figure. Label the net with its
appropriate dimensions.
11.
(2x 33)
12. Find the perimeter of the polygon.
3
6 in.
x
12. y
* )
D
2
7
(2x)
C
24
13.
(3x) 10
10 in.
13
x
3
14
34
5. Find the slope of a (3x
lineparallel
10) to AB with
A(4, 6) and B(-3, 8).
13. Find the measure of ⬔TQM.
R
6.
Find
value of xfor
if AC
=D
16.and E without using any new variables.
Give
thethe
coordinates
points
the
2 coordinates
5x 10 of the midpoint of DE.
Then 3x
find
x 4)
A
B
C
Q
14. rectangle
(3
15. isosceles trapezoid
T
(2x 16. rhombus
9)
7. Find the value of x.
M
G (a, c) E
(4x 10)
D
E
(3x 5)
F (b, 0)
D
8. Construct the perpendicular bisector of LM.
L
D
F (a, b)
E the
14. Writing Write a paragraph proof for
following statement:
C (a, 0)
If 2x + 4 = 6, then x = 1. B (0, b)
G (a c, 0)
15. Find the intersection of planes ABC
and LMO.
L
M
A
Geometry
Chapterjustifies
6
9.
What property
the following
statement?
If 4x + 6 = 20, then 4x = 14.
C
B
Form A Test
27
MO
191
Geometry Chapters 1–3
38.
y
V
110
Quarter 1 Test
35. m 2;
y-int. 1
z
2m
11. Find the measure of ⬔1.
9.
2 in.
Determine whether AB and CD are parallel, perpendicular, or neither.
neither
40. A(-1, -4), B(2, 11), C(1, 1), D(4, 10) 41. A(2, 8), B(-1, -2), C(3, 7), D(0, -3) n
© Pearson Education, Inc. All rights reserved.
* )
To relate slope and
perpendicular lines
U
Right
Find the values of the variables for each figure.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
To relate slope and
parallel lines
1
31in.
3. Classify the triangle by its angles.
The product of the slopes of two nonvertical perpendicular lines is -1. In a plane,
every vertical line is perpendicular to every horizontal line.
2
4 in.
V
39
y
O
2
4
x
2
2
4
191