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SECTION 1
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Trusted Content
Common Core State Standards
W
ith American students fully prepared for the future, our
communities will be best positioned to compete successfully
in the global economy. — Common Core State Standards Initiative
What is the goal of the Common Core
State Standards?
The mission of the Common Core State Standards is to provide a consistent, clear understanding
of what students are expected to learn, so teachers and parents know what they need to do to
help them. The standards are designed to be robust and relevant to the real world, reflecting the
knowledge and skills that students need for success in college and careers.
Who wrote the standards?
The National Governors Association Center for Best Practices
and the Council of Chief State School Officers worked with
representatives from participating states, a wide range of
educators, content experts, researchers, national organizations,
and community groups.
ongruent Triangles
At the high school level the Common Core State Standards are
organized by conceptual category. To ease implementation four
model course pathways were created: traditional, integrated,
accelerated traditional and accelerated integrated. Glencoe
Algebra 1, Glencoe Geometry, and Glencoe Algebra 2 follow
the traditional pathway.
What are the major points of the standards?
The standards seek to develop both students’ mathematical
understanding and their procedural skill. The Standards for
Mathematical Practice describe varieties of expertise that
mathematics teachers at all levels should seek to develop in
their students. The Standards for Mathematical Content define
what students should understand and be able to do at each
level in their study of mathematics.
Mathematical
Content
Unit 2
|
Congruence
Coongru
Congruent
C
ongrrue Triangles
riangles
G.CO.12
Mathematical
Content
Get Ready for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
How do I implement the standards?
The Common Core State Standards are shared goals and
expectations for what knowledge and skills your students need to
succeed. You as a teacher, in partnership with your colleagues,
principals, superintendents, decide how the standards are to be
met. Glencoe Geometry is designed to help you devise lesson
plans and tailor instruction to the individual needs of the students
in your classroom as you meet the Common Core State
Standards.
4-1 Classifying Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
G.CO.12
Explore: Geometry Lab Angles of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
G.CO.12
4-2 Angles of Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
G.CO.10
4-3 Congruent Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
G.CO.7, G.SRT.5
4-4 Proving Triangles Congruent—SSS, SAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
G.CO.10, G.SRT.5
Extend: Geometry Lab Proving Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
G.CO.12, G.SRT.5
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
4-5 Proving Triangles Congruent—ASA, AAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Extend: Geometry Lab Congruence in Right Triangles . . . . . . . . . . . . . . . . . . . . . . . . . 283
4-6 Isosceles and Equilateral Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
G.CO.10, G.SRT.5
G.SRT.5
G.CO.10, G.CO.12
Explore: Graphing Technology Lab Congruence Transformations. . . . . . . . . . . . . . . . . 294
G.CO.5, G.CO.6
4-7 Congruence Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
G.CO.6, G.CO.7
4-8 Triangles and Coordinate Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
G.CO.10, G.GPE.4
Scott Markewitz/Getty Images
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Preparing for Standardized Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
Standardized Test Practice, Chapters 1–4 . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Virtual
Manipulatives
Graphing
Calculator
pp. 206, 273
pp. 187, 294
Foldables
pp. 172, 236
Self-Check
Practice
pp. 182, 258
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Domain Names
How do I decode the standards?
This diagram provides clarity for decoding the standard identifiers.
Abbreviations
Congruence
C
CO
Similarity, Right Triangles, and
Trigonometry
SRT
Points, Lines,
C and Pla
Circles
G.SRT.2
Conceptual Category
G = Geometry
S = Statistics and
Probability
Domain
Standard
There are numerous tools for implementing the Common Core
State Standards available throughout the program, including:
Standards at point-of-use in the Chapter Planner and in each
lesson of the Teacher Edition,
Complete standards coverage in Glencoe Geometry ensures
that you have all the content you need to teach the standards,
f Triangles
C
Content
Standards
G.CO.12 Make formal geometric construc
and methods (compass andGeometr
straightedge,
Geometry
G
eometry
Lab
Angles
Angles
gles
ess software
of Tr
Trian
Triangles
Tria
i ngl
paper folding, dynamic geometric
Mathematical Practices 5
Explore 4-2
GMD
Modeling with Geometry
MG
Conditional Probability and the Rules
of Probability
CP
Using Probability to Make Decisions
MD
Correlations that show at a glance where each standard is
addressed in Glencoe Geometry.
You can also visit connectED.mcgraw-hill.com to learn more
about the Common Core State Standards. There you can choose
from an extensive collection of resources to use when planning
instruction.
Step 3
You used basic
geometric concepts
and properties to
solve problems.
protractor
scissors
For each triangle, fold vertex B
down so that the fold line is
−−
parallel to AC. Relabel as vertex B.
Identify intersecting
in
liness and planes.
1
N
ewV
V b l
Vo
New
Vocabulary
Advise students to label the obtuse
angle B when they are first working
through Activity 1. They should also
repeat Activity 1 using acute, right,
and equilateral triangles to further
verify concepts.
Then fold vertices A and C so that
they meet vertex B. Relabel as
vertices A and C.
Identify and model
points, lines, and
planes.
New Vocabulary is listed at the
beginning of every lesson.
Teaching Tip
Draw and cut out several different
triangles. Label the vertices A, B,
and C.
2 Teach
2. Make a conjecture about the sum of the measures of the interior angles of a triangle.
The sum of the measures of the angles of any triangle is 180.
Activity 2 Exterior Angles of a Triangle
Step 2
Unfold each triangle from Activity 1
and place each on a separate piece
−−
of paper. Extend AC as shown.
Step 3
Arrange ∠A and ∠B so that they
fill the angle adjacent to ∠C as
shown.
For each triangle, tear off
∠A and ∠B.
Model and Analyze the Results
m∠A + m∠B is the measure of
Ed-Imaging
3. The angle adjacent to ∠C is called an exterior angle of triangle ABC. Make a
the exterior angle at C.
conjecture about the relationship among ∠A, ∠B, and the exterior angle at C.
4. Repeat the steps in Activity 2 for the exterior angles of ∠A and ∠B in each triangle. See students’ work.
5. Make a conjecture about the measure of an exterior angle and the
sum of the measures of its nonadjacent interior angles. See margin.
connectED.mcgraw-hill.com
3 Assess
0245_GEO_S_C04_EXP2_663929.indd
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Formative Assessment
In Exercises 1–5, students determine angle
measures of the triangles used in this activity,
find relationships, and make conjectures that will
lead them to the Angle-Sum Theorem and the
Exterior Angle Theorem.
From Concrete to Abstract
245
5/10/12
Example
, line QP or QP
line m, line PQ or PQ
P
Q
B
D
C
a capital script letter or by the letters naming
three points that are not all on the same line
Ask:
What are some other objects that
points, lines, and planes could be
used to represent? Sample response:
Stars can be represented by points,
lines can be used to connect the stars
to form constellations, and a plane can
be used to represent the sky.
m
K
plane K, plane BCD, plane CDB, plane DCB,
plane DBC, plane CBD, plane BDC
connectED.mcgraw-hill.com
What are some other ways that
combinations of points, lines, and
planes are used? networks and
maps
(continued on the next page)
5
Lesson 1-1 Resources
Resource
Approaching Level AL
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Teacher Edition
Additional Answer
5. The measure of an exterior angle is
equal to the sum of the measures of
the two nonadjacent interior angles.
Chapter
Resource
Masters
On Level OL
Study Guide and Intervention, pp. 5–6
Skills Practice, p. 7
Practice, p. 8
Word Problem Practice, p. 9
Graphing Calculator Activity, p. 11
5-Minute Check 1-1
Study Notebook
Teaching Geometry with Manipulatives
245
Study Guide and Intervention, pp. 5–6
Skills Practice, p. 7
Practice, p. 8
Word Problem Practice, p. 9
Enrichment, p. 10
Graphing Calculator Activity, p. 11
5-Minute Check 1-1
Study Notebook
Teaching Geometry with Manipulatives
Differentiated Instruction, p. 10
English Learners ELL
Differentiated Instruction, pp. 10, 11
5/9/12 3:24 PM
Beyond
Level BL
Differentiated Instruction, pp. 10, 11
12-5-23
Example
Collinear points are points that lie on the same line. Noncollinear points do not lie on the
same line. Coplanar points are points that lie in the same plane. Noncoplanar points do
not lie in the same plane.
Other
0245_GEO_T_C04_EXP2_663930.indd 245
the letters representing two points on the line
or a lowercase script letter
Example
Have students read the Why? section
of the lesson.
point A
Named by
Named by
When you change the angle
measures, what seems to be the
constant? the sum of the angles
connectED.mcgraw-hill.com
2 Teach
Scaffolding Questions
A
a capital letter
A plane is a flat surface made up of points that extends
infinitely in all directions. There is exactly one plane
through any three points not on the same line.
When you change a triangle from an
acute triangle to an obtuse triangle,
how does it affect the other angle
measures? the other angle measures
get smaller
plane
x
point
A line is made up of points and has no thickness or width.
There is exactly one line through any two points.
4 Model with mathematics.
6 Attend to precision.
Practice Have students complete
Activity 2 and Model and Analyze the
Results 3–5.
Students can further explore and conjecture
about the relationships of the side and angle
measures of the small triangle formed when
vertex B is folded down in Activity 1. Students
should see that although the side lengths are not
the same, the angle measures are congruent.
line
O
A point is a location. It has neither shape nor size.
Named by
Mathematical Practices
Ask:
What is a commonality of all
triangles? They all have three sides
and three vertices.
After Lesson 1-1 Use numeric and
geometric patterns to make
generalizations about geometric
properties, including properties of
polygons.
y
KeyConcept Undefined Terms
G.CO.1 Know precise
definitions of angle, circle,
perpendicular line, parallel
line, and line segment, based
on the undefined notions of
point, line, distance along a
line, and distance around a
circular arc.
Brand X Pictures/Jupiterimages
Step 1
Lesson 1-1 Identify and model
points, lines, and planes. Identify
intersecting lines and planes.
Po
Points, Lines, and Planes Unlike the real-world objects that they model, shapes,
The phrase exactly one in a statement such as,
“There is exactly one line through any two
points,” means that there is one and only one.
Content Standards
Arrange students in groups of 3 or 4,
mixing abilities. Then have groups
complete Activity 1 and Analyze the
Results 1 and 2.
Before Lesson 1-1 Use geometric
concepts and properties to solve
problems.
You are already familiar with the terms point,
line, and plane from algebra. You graphed on
a coordinate plane and found ordered pairs
that represented points on lines. In geometry,
these terms have a similar meaning.
Common Core
State Standards
Working in Cooperative Groups
VerticalAlignment
On a subway
subw map, the locations of
stops are represented
r
by points. The
t
route the train
can take is modeled
by a series of connected paths that
li
look like lines.
The flat surface of
o which these points and
the map on
lines lie is representative of a plane.
points, lines, and planes do not have any actual size. In geometry, point, line, and
plane are considered undefined terms because they are only explained using examples
and descriptions.
undefined term
point
line
plane
collinear
coplanar
intersection
definition
defined term
space
Analyze the Results
1. Angles A, B, and C are called interior angles of triangle ABC. What type of figure do
these three angles form when joined together in Step 3? a straight angle or straight line
1 Focus
Then
Now
hyy?
?
definitions
of angle,
circleWWhy?
perpendicular 1line, paralle
li
d li 2
t b
Materials
Lesson 1-1
Points,
P
oints, Lines,
Linees, and Planes
G.CO.1 Know precise
1 Focus
A ti it 1 Interio
Activity
IInterior
t i r Angles
A l off a TTriangle
Tr
Triiangle
l
Step 2
Geometric Measurement and
Dimension
Content Standards
Objective Find the relationships among
the measures of the interior angles of
a triangle.
Common Core State Standards
C
Content Standards
C
G.CO.12 Make formal geometric constructions with a variety of tools
and methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.).
Mathematical Practices 5
Step 1
GPE
Common Core
State Standards
Common Core State Standards
C
In this lab, you will find special relationships among the angles of a triangle.
Expressing Geometric Properties
with Equations
Practice, p. 8
Word Problem Practice, p. 9
Enrichment, p. 10
Graphing Calculator Activity, p. 11
5-Minute Check 1-1
Study Notebook
Differentiated Instruction, p. 10
Study Guide and Intervention, pp. 5–6
Skills Practice, p. 7
Practice, p. 8
Word Problem Practice, p. 9
Graphing Calculator Activity, p. 11
5-Minute Check 1-1
Study Notebook
Teaching Geometry with Manipulatives
connectED.mcgraw-hill.com
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T11
SECTION 1
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Trusted Content
Common Core State Standards
Common Core State Standards, Traditional
Geometry Pathway, Correlated to
Glencoe Geometry, Common Core Edition
Lessons in which the standard is the primary focus are indicated in bold.
Student Edition
Lesson(s)
Standards
Student Edition
Page(s)
Geometry
Congruence G-CO
Experiment with transformations in the plane.
1. Know precise definitions of angle, circle, perpendicular line, parallel
line, and line segment, based on the undefined notions of point, line,
distance along a line, and distance around a circular arc.
1-1, 1-2, 1-3, 1-4, 3-1, 3-2,
10-1
5–12, 14–21, 25–35, 36–44,
173–178, 180–186, 697–705
2. Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that
take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch).
4-7, 7-6, 9-1, 9-2,
Explore 9-3, 9-3,
Explore 9-4, 9-4, 9-6
296–302, 511–517, 623–631,
632–638, 639, 640–646, 650,
651–659, 674–681
3. Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
9-5
663–669
4. Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line segments.
9-1, 9-2, 9-3, Explore 9-4,
9-4
623–631, 632–638, 640–646,
650, 651–659
5. Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper,
or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
Explore 4-7, 9-1, 9-2,
Explore 9-3, 9-3,
Explore 9-4, 9-4
294–295, 623–631, 632–638,
639, 640–646, 650, 651–659
Understand congruence in terms of rigid motions.
6. Use geometric descriptions of rigid motions to transform figures and
to predict the effect of a given rigid motion on a given figure; given
two figures, use the definition of congruence in terms of rigid
motions to decide if they are congruent.
Explore 4-7, 4-7, 9-1, 9-2,
9-3, 9-4, Extend 9-6
294–295, 296–302, 623–631,
632–638, 640–646, 651–659,
682–683
7. Use the definition of congruence in terms of rigid motions to show
that two triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent.
4-3, Explore 4-7, 4-7, 9-1,
9-2, 9-3, 9-4, Extend 9-6
255–263, 294–295, 296–302,
623–631, 632–638, 640–646,
651–659, 682–683
8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions.
4-7, Extend 9-6
296–302, 682–683
(+) Advanced Mathematics Standards
T12
Mathematical Modeling Standards
Correlation
Standards
Student Edition
Lesson(s)
Student Edition
Page(s)
Prove geometric theorems.
9. Prove theorems about lines and angles.
2-7, 2-8, 3-2, 3-5, 5-1
144–150, 151–159, 180–186,
207–214, 324–333
10. Prove theorems about triangles.
4-2, 4-3, 4-4, 4-5, 4-6, 4-8,
5-1, 5-2, 5-3, 5-4, 5-5, 5-6,
7-4, Explore 8-2
246–254, 255–263, 264–272,
275–282, 285–293, 303–309,
324–333, 335–343, 344–351,
355–362, 371–380, 490–499,
546
11. Prove theorems about parallelograms.
6-2, 6-3, 6-4, 6-5
403–411, 413–421, 423–429,
431–438
Make geometric constructions.
12. Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.).
1-2, 1-3, 1-4, Extend 1-5,
Extend 1-6, 2-7, Explore 3-2,
3-5, 3-6, 4-1, Explore 4-2,
4-4, Extend 4-4, 4-5, 4-6,
Explore 5-1, Explore 5-2,
Explore 5-5, Explore 6-3,
6-3, 6-4, 6-5, 7-4, 9-1,
Explore 9-3, Extend 9-5,
10-3, 10-5, Extend 10-5
14–21, 25–35, 36–44, 55,
65–66, 144–150, 179,
207–214, 215–224, 237–244,
245, 264–272, 273, 275–282,
285–293, 323, 334, 363, 412,
413– 421, 423–429, 430– 438,
490– 499, 623–631, 639,
670– 671, 715–722, 732–739,
740
13. Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
Extend 10-5
740
Similarity, Right Triangles, and Trigonometry G-SRT
Understand similarity in terms of similarity transformations.
1. Verify experimentally the properties of dilations given by a center and
a scale factor:
a. A dilation takes a line not passing through the center of the
dilation to a parallel line, and leaves a line passing through the
center unchanged.
Explore 9-6, 9-6
672– 673, 674–681
b. The dilation of a line segment is longer or shorter in the ratio given
by the scale factor.
Explore 9-6, 9-6
672– 673, 674–681
2. Given two figures, use the definition of similarity in terms of
similarity transformations to decide if they are similar; explain using
similarity transformations the meaning of similarity for triangles as
the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
7-2, 7-3, 7-6, Extend 9-6
469– 477, 478–487, 511–517,
682– 683
3. Use the properties of similarity transformations to establish the
AA criterion for two triangles to be similar.
7-3, 7-6, Extend 9-6
478–487, 511–517, 682–683
Prove theorems involving similarity.
4. Prove theorems about triangles.
7-3, 7-4, 7-5, 8-1
478–487, 490–499, 501–508,
537–545
connectED.mcgraw-hill.com
T13
SECTION 1
|
Trusted Content
Common Core State Standards
Continued
Student Edition
Lesson(s)
Standards
Student Edition
Page(s)
5. Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
4-3, 4-4, Extend 4-4, 4-5,
Extend 4-5, 7-3, 7-4, 7-5,
7-6, 8-1
255–263, 264–272, 273,
275–282, 283–284, 478–487,
490–499, 501–508, 511–517,
537–545
Define trigonometric ratios and solve problems involving right triangles.
6. Understand that by similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
8-3, Explore 8-4, 8-4, Extend
8-4
558–566, 567, 568–577, 578
7. Explain and use the relationship between the sine and cosine of
complementary angles.
8-4
568–577
8. Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
8-2, 8-4, 8-5, 8-6
547–555, 568–577, 580–587,
588–597
Apply trigonometry to general triangles.
1
9. (+) Derive the formula A = _
abb sin (C ) for the area of a triangle
8-6
588–597
10. (+) Prove the Laws of Sines and Cosines and use them to solve
problems.
8-6
588–597
11. (+) Understand and apply the Law of Sines and the Law of Cosines
to find unknown measurements in right and non-right triangles
(e.g., surveying problems, resultant forces).
8-6, Extend 8-6
588–597, 598
2
by drawing an auxiliary line from a vertex perpendicular to the
opposite side.
Circles G-C
Understand and apply theorems about circles.
1. Prove that all circles are similar.
10-1
697–705
2. Identify and describe relationships among inscribed angles, radii,
and chords.
10-1, 10-2, 10-3, 10-4, 10-5
697–705, 706–714, 715–722,
723–730, 732–739
3. Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.
10-4, Extend 10-5
723–730, 740
4. (+) Construct a tangent line from a point outside a given circle to
the circle.
10-5
732–739
Find arc lengths and areas of sectors of circles.
5. Derive using similarity the fact that the length of the arc intercepted
by an angle is proportional to the radius, and define the radian
measure of the angle as the constant of proportionality; derive the
formula for the area of a sector.
10-2, 11-3
706–714, 798–804
(+) Advanced Mathematics Standards
T14
Mathematical Modeling Standards
Correlation
Student Edition
Lesson(s)
Standards
Student Edition
Page(s)
Expressing Geometric Properties with Equations G-GPE
Translate between the geometric description and the equation for a
conic section.
1. Derive the equation of a circle of given center and radius using the
Pythagorean Theorem; complete the square to find the center and
radius of a circle given by an equation.
10-8
757–763
2. Derive the equation of a parabola given a focus and directrix.
Extend 10-8
764–765
Use coordinates to prove simple geometric theorems algebraically.
4. Use coordinates to prove simple geometric theorems algebraically.
4-8, 6-2, 6-3, 6-4, 6-5, 6-6,
10-8
303–309, 403–411, 413–421,
423–429, 430–438, 439–448,
757–763
5. Prove the slope criteria for parallel and perpendicular lines and use them
to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
Explore 3-3, 3-3, 3-4, Extend
3-4, Extend 7-3
187, 188–196, 198–205, 206,
488–489
6. Find the point on a directed line segment between two given points
that partitions the segment in a given ratio.
1-3, 7-4, 8-7, 9-6, 10-8
25–35, 490–499, 600–608,
674–681, 757–763
7. Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.
1-6, 11-1
56–64, 779–786
Geometric Measurement and Dimension G-GMD
Explain volume formulas and use them to solve problems.
1. Give an informal argument for the formulas for the circumference of
a circle, area of a circle, volume of a cylinder, pyramid, and cone.
10-1, 11-3, 12-4, 12-5, 12-6
697–705, 798–804, 863–870,
873–879, 880–887
3. Use volume formulas for cylinders, pyramids, cones, and spheres to
solve problems.
1-7, 12-4, 12-5, 12-6
67–74, 863–870, 873–879,
880–887
Visualize relationships between two-dimensional and three-dimensional
objects.
4. Identify the shapes of two-dimensional cross-sections of threedimensional objects, and identify three-dimensional objects
generated by rotations of two-dimensional objects.
Extend 9-3, 12-1
647–648, 839–844
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T15
SECTION 1
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Trusted Content
Common Core State Standards
Continued
Student Edition
Lesson(s)
Standards
Student Edition
Page(s)
Modeling with Geometry G-MG
Apply geometric concepts in modeling situations.
1. Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a
cylinder).
Throughout the text; for
example, Extend 1-1, Extend
1-7, 6-1, 11-5, 12-3
Throughout the text; for
example, 13, 75–77,
393–401, 818–824, 854–862
2. Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot).
Extend 11-2, 12-4, 12-5
797, 863–870, 873–879
3. Apply geometric methods to solve problems (e.g., designing an
object or structure to satisfy physical constraints or minimize cost;
working with typographic grid systems based on ratios).
2-5, 3-6, 5-1, 5-2, 5-5, 6-6,
7-1, 7-7, 8-2, 10-3, 11-2,
11-4, 12-2, 12-4, 12-6, 13-4
127–134, 215–224, 324–333,
335–343, 364–370, 439–448,
461–467, 518–523, 547–555,
715–722, 789–796, 807–815,
846–853, 863–870, 880–887,
939–946
Statistics and Probability
Conditional Probability and the Rules of Probability S-CP
Understand independence and conditional probability and use them to
interpret data.
1. Describe events as subsets of a sample space (the set of outcomes)
using characteristics (or categories) of the outcomes, or as unions,
intersections, or complements of other events (“or,” “and,” “not”).
13-5, 13-6
947–953, 956–963
2. Understand that two events A and B are independent if the
probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are
independent.
13-5
947–953
13-5
947–953
4. Construct and interpret two-way frequency tables of data when two
categories are associated with each object being classified. Use the
two-way table as a sample space to decide if events are
independent and to approximate conditional probabilities.
Extend 13-5
954–955
5. Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations.
13-5
947–953
P (A
(A and B )
3. Understand the conditional probability of A given B as _,
P (B )
and interpret independence of A and B as saying that the conditional
probability of A given B is the same as the probability of A, and the
conditional probability of B given A is the same as the probability of B.
(+) Advanced Mathematics Standards
T16
Mathematical Modeling Standards
Correlation
Student Edition
Lesson(s)
Standards
Student Edition
Page(s)
Use the rules of probability to compute probabilities of compound
events in a uniform probability model.
6. Find the conditional probability of A given B as the fraction of B ’s
outcomes that also belong to A, and interpret the answer in terms of
the model.
13-5, Extend 13-5
947–953, 954–955
7. Apply the Addition Rule, P (A
(A or B ) = P (A
(A) + P (B ) - P (A
(A and B ),
and interpret the answer in terms of the model.
13-6
956–963
8. (+) Apply the general Multiplication Rule in a uniform probability
model, P (A
(A and B)
B = P (A
(A)P (B |A ) = P (B )P (A
( |B ), and interpret the
answer in terms of the model.
13-5
947–953
9. (+) Use permutations and combinations to compute probabilities of
compound events and solve problems.
13-2
922–930
Using Probability to Make Decisions S-MD
Use probability to evaluate outcomes of decisions.
6. (+) Use probabilities to make fair decisions (e.g., drawing by lots,
using a random number generator).
0-3, 13-4
P8–P9, 939–946
7. (+) Analyze decisions and strategies using probability concepts (e.g.,
product testing, medical testing, pulling a hockey goalie at the end of
a game).
0-3, 13-3, 13-5
P8–P9, 931–937, 947–953
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T17
SECTION 1
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Trusted Content
Common Core State Standards
Common Core State Standards for
Mathematical Practice, Correlated to
Glencoe Geometry, Common Core Edition
1. Make sense of problems and persevere in solving them.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Lessons 1-5, 2-1, 3-5, 4-5, 5-4, 6-1, 7-5, 8-2, 9-5, 10-2, 11-2, 12-6, and 13-5.
2. Reason abstractly and quantitatively.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
1-3, 2-7, 3-6, 4-2, 5-3, 6-4, 7-7, 8-4, 9-6, 10-6, 11-4, Extend 12-4, and 13-2.
3. Construct viable arguments and critique the reasoning of others.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Lessons 1-7, 2-5, 3-5, 4-4, 5-4, 6-6, 7-4, 8-3, 9-1, 10-1, 11-5, 12-4, and 13-3.
4. Model with mathematics.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Lessons 1-1, 2-3, 3-1, 4-7, 5-6, 6-5, 7-7, 8-7, 9-3, 10-1, 11-4, 12-3, and 13-3.
5. Use appropriate tools strategically.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Extend 1-6, 2-7, Explore 3-3, Explore 4-7, Explore 5-5, Extend 6-1, 7-4, Explore 8-4, Explore 9-4, Extend 10-5, Explore 11-2,
and Extend 12-4.
6. Attend to precision.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Extend 1-2, Lessons 2-7, 3-3, 4-4, 5-1, 6-2, 7-3, 8-1, 9-2, 10-3, 11-3, 12-5, and 13-2.
7. Look for and make use of structure.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Lessons 1-3, 2-1, 3-6, 4-1, Explore 5-5, 6-1, Extend 7-1, Explore 8-4, 9-5, 10-6, 11-4, 12-2, and 13-1.
8. Look for and express regularity in repeated reasoning.
Glencoe Geometryy exhibits these practices throughout the entire program. Some specific lessons for review are:
Lessons 1-3, 2-1, Explore 3-3, 4-6, 5-3, 6-1, 7-1, 8-4, Explore 9-3, Extend 10-8, Extend 11-2, Explore 12-1, and 13-1.
T18