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BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard
# and
Identifier
(AHSGEReview)
Content Standard Description
**AHSGE – REVIEW (if needed)
Modeling
With
Geometry
39
[G-MG1]
39. Use geometric shapes, their
measures, and their properties to
describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder).* [G-MG1]
Congruence
1
[G-CO1]
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. [G-CO1]
Page 1 of 28
1st 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
VII-6
II-1
II-4
II-3
VII-2
Standards for Quality Core
Mathematical Prerequisites
Practice
Skill
Algebra 2
D.1.a
E.1.h
IV-2
VII-1
C.1.a
Textbook Resources
Glencoe - Geometry
0-3 Simple Probability
0-4 Algebraic Expressions
0-5 Linear Equations
0-6 Linear Inequalities
0-8 Systems of Linear
Equations
0-9 Simplifying Radicals
1-1 Extend Lab (Describing
What You See)
6
1-1
1-2
1-3
1-4
1-5
Points, Lines, Planes
Linear Measure
Distance and Midpoint
Angle Measure
Angle Relationships
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Congruence
Content
Content Standard Description
Standard
# and
Identifier
12
12. Make formal geometric
[G-CO12] constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective
devices, paper folding, and dynamic
geometric software. [G-CO12]
1st 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
IV-2
D.1.a
VII-1 D.1.c
D.1.d
Standards for Quality Core
Mathematical Prerequisites
Practice
Skill
5
6
Textbook Resources
Glencoe - Geometry
1-2 Linear Measure
1-3 Distance and Midpoint
1-4 Angle Measure
1-5 Extend Lab
Constructing
Perpendiculars
1-6 Extend Lab 2-D Figures
Expressing
Geometric
Properties with
Equations
32
[G-GPE6]
32. Find the point on a directed line
segment between two given points
that partitions the segment in a
given ratio. [G-GPE6]
IV-2
G.1.c
2
7
8
Algebra 2
1-3 Distance and Midpoint
Expressing
Geometric
Properties with
Equations
33
[G-GPE7]
IV-1,2
F.2.a
G.1.c
1-6 Two-Dimensional
Figures
36
[GGMD3]
IV-1,2
D.4.a
F.2.a
F.2.c
1
2
5
6
1
2
3
4
5
Algebra 2
Geometric
Measurement
and
Dimension
33.) Use coordinates to compute
perimeters of polygons and areas of
triangles and rectangles, e.g., using
the distance formula.* [G-GPE7]
36.) Use volume formulas for
cylinders, pyramids, cones, and
spheres to solve problems.* [GGMD3]
Page 2 of 28
1-7 Three – Dimensional
Figures
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Modeling
with
Geometry
Content
Content Standard Description
Standard
# and
Identifier
39
39.) Use geometric shapes, their
[G-MG1] measures, and their properties to
describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder).* [G-MG1]
Prep
Modeling
with
Geometry
Congruence
41
[G-MG3]
9
[G-CO9]
Congruence
12
[G-CO12]
Page 3 of 28
1st 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
D.1.a
E.1.h
Standards for Quality Core
Mathematical Prerequisites
Practice
Skill
4
5
7
**These lessons are not on the course
of study. They are to prep for the
objectives that will be covered in
lessons 2.5 -2.8
9. Prove theorems about lines and
angles. [G-CO9]
12. Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software. [G-CO12]
1-7 Extend 2-D
Representations of 3-D
Objects
Algebra 2
PreCalculus
41. Apply geometric methods to solve
design [G-MG3]
VII-1
C.1.a
C.1.b
C.1.e
D.1.b
D.1.c
D.1.a
D.1.c
D.1.d
1
4
5
2
3
5
5
6
Textbook Resources
Glencoe - Geometry
2-1 – 2-4, 2-6 (Prep for 2-5
– 2.8)
2-5 Postulates and
Paragraph Proofs
Algebra 2
PreCalculus
2-7 Proving Segment
Relationships
2-8 Proving Angle
Relationships
2-7 Proving Segment
Relationships
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard
# and
Identifier
Congruence
1
[G-CO1]
Congruence
9
[G-CO9]
Congruence
12
[G-CO12]
Expressing
Geometric
Properties
with
Equations
Modeling
with
Geometry
Page 4 of 28
31
[G-GPE5]
41
[G-MG3]
Content Standard Description
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. [G-CO1]
9.) Prove theorems about lines and
angles. [G-CO9]
1st 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
VII-1 C.1.a
VII-1
12.) Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software. [G-CO12]
IV-2
31.) 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). [G-GPE5]
IV-2
41.) Apply geometric methods to solve
design [G-MG3]
IV-2
Standards for Quality Core
Mathematical Prerequisites
Practice
Skill
6
Textbook Resources
Glencoe - Geometry
3-1 Parallel Line and
Transversals
3-2 Angles and Parallel
Lines
C.1.a
C.1.b
C.1.e
D.1.b
D.1.c
D.1.a
D.1.c
D.1.d
2
3
5
Algebra 2
PreCalculus
C.1.d
D.1.f
G.1.a
G.1.c
3
8
Algebra 2
PreCalculus
3-3 Explore (Investigating
Slope)
3-3 Slopes of Lines
3-4 Extend (Equations of
Perpendicular Bisectors)
3-4 Equations of Lines
1
4
5
Algebra 2
PreCalculus
3-6 Perpendiculars and
Distance
5
6
3-2 Angles and Parallel
Lines
3-5 Proving Lines Parallel
3-2 Explore (Angles and
Parallel Lines)
3-5 Proving Lines Parallel
3-6 Perpendiculars and
Distance
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
2nd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
VII-4
D.1.a
D.1.c
D.1.d
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
12
[G-CO12]
12.) Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software. [G-CO12]
Congruence
10
[G-CO10]
10.) Prove theorems about triangles.
[G-CO10]
VII-4
C.1.e
D.2.b
D.2.j
2
3
5
Congruence
7
[G-CO7]
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. [G-CO7]
VII-4
C.1.g
E.1.b
3
Page 5 of 28
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
4-1 Classifying Triangles
4-2 Explore Angles of Triangles
4-4 Extend Proving
Constructions
4-4 Proving Triangles Congruent
(SSS/SAS)
4-5 Proving Triangles Congruent
(ASA/AAS)
4-6 Isosceles and Equilateral
Triangles
5
6
Algebra 2
PreCalculus
4-2 Angles of Triangles
4-3 Congruent Triangles
4-4 Proving Triangles Congruent
(SSS/SAS)
4-5 Proving Triangles Congruent
(ASA/AAS)
4-6 Isosceles and Equilateral
Triangles
4-8 Triangles and Coordinate
Proof
4-3 Congruent Triangles
4-7 Explore Congruence
Transformations
4-7 Congruence
Transformations
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Similarity,
Right
Triangles,
and
Trigonometry
18
[G-SRT5]
18.) Use congruence and similarity
criteria for triangles to solve problems
and to prove relationships in
geometric figures. [G-SRT5]
Congruence
5
[G-CO5]
Congruence
6
[G-CO6]
Page 6 of 28
2nd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
D.2.d
E.1.e
E.1.g
3
4
6
7
Algebra 2
PreCalculus
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. [GCO5]
E.1.a
E.1.e
3
5
7
4-3 Congruent Triangles
4-4 Extend Proving
Constructions
4-4 Proving Triangles Congruent
(SSS/SAS)
4-5 Extend Congruence in Right
Triangles
4-5 Proving Triangles Congruent
4-7 Explore Congruence
Transformations
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. [GCO6]
E.1.a
3
5
7
VII-4
4-7 Explore Congruence
Transformations
4-7 Congruence
Transformations
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
2nd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
2
[G-CO2]
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). [G-CO2]
G.1.e
5
6
4-7 Congruence
Transformations
Congruence
8
[G-CO8]
8.) Explain how the criteria for triangle
congruence, angle-side-angle (ASA),
side-angle-side (SAS), and side-sideside (SSS), follow from the definition
of congruence in terms of rigid
motions. [G-CO8]
C.1.f
2
3
4-7 Congruence
Transformations
Expressing
Geometric
Properties
with
Equations
30
[G-GPE4]
30.) Use coordinates to prove simple
geometric theorems algebraically. [GGPE4]
G.1.b
G.1.c
2
3
7
Algebra 2
Congruence
9
. [G-CO9]
9.) Prove theorems about lines and
angles. [G-CO9]
C.1.a
C.1.b
C.1.e
D.1.b
D.1.c
2
3
5
Algebra 2
PreCalculus
Page 7 of 28
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
4-8 Triangles and Coordinate
Proof
5-1Bisectors of Triangles
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
2nd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
10
. [G-CO10]
10.) Prove theorems about triangles.
[G-CO10]
Congruence
12
[G-CO12]
12.) Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software. [G-CO12]
Modeling
with
Geometry
41
[G-MG3]
41.) Apply geometric methods to solve
design [G-MG3]
VII-4
Modeling
with
Geometry
39
[G-MG1]
39.) Use geometric shapes, their
measures, and their properties to
describe objects (e.g., modeling a tree
trunk or a human torso as a cylinder).*
[G-MG1]
VII-3
Page 8 of 28
VII-4
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
C.1.e
D.2.b
D.2.j
2
3
5
Algebra 2
PreCalculus
5-1 Bisectors of Triangles
5-2 Medians and Altitudes
5-3 Inequalities in One Triangle
5-4 Indirect Proof
5-5Triangle Inequality
5-6 Inequalities in Two Triangles
D.1.a
D.1.c
D.1.d
5
6
5-1 Explore Constructing
Bisectors
5-2 Explore Constructing
Medians and Altitudes
5-5 Explore Triangle Inequality
1
4
5
5-1 Bisectors of Triangles
5-2 Medians and Altitudes of
Triangles
5-5 Triangle Inequality
4
5
7
6-1 Angles of Polygons
D.1.a
E.1.h
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
2nd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
11
[G-CO11]
VII-3
Congruence
12
. [G-CO12]
Expressing
Geometric
Properties
with
Equations
30
[G-GPE4]
11.) Prove theorems about
parallelograms. Theorems include
opposite sides are congruent, opposite
angles are congruent; the diagonals of
a parallelogram bisect each other; and
conversely, rectangles are
parallelograms with congruent
diagonals. [G-CO11]
12.) Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software. [G-CO12]
30.) Use coordinates to prove simple
geometric theorems algebraically. [GGPE4]
Modeling
with
Geometry
41
[G-MG3]
41.) Apply geometric methods to
solve design problems (e.g.,
designing an object or structure to
satisfy physical constraints or
minimize cost, working with
typographic grid systems based on
ratios).* [G-MG3]
VII-3
Page 9 of 28
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
C.1.e
C.1.i
D.2.j
2
3
5
Algebra 2
PreCalculus
VII-3
D.1.a
D.1.c
D.1.d
5
6
VII-3
G.1.b
2
3
7
G.1.c
1
4
5
Textbook Resources
6-2 Parallelograms
6-3 Tests for Parallelograms
6-4 Rectangles
6-5 Rhombi and Squares
6-3 Explore Parallelograms
6-3 Tests for Parallelograms
6-4 Rectangles
6-5 Rhombi and Squares
Algebra 2
6-2 Parallelograms
6-3 Tests for Parallelograms
6-4 Rectangles
6-5 Rhombi and Squares
6-6 Trapezoids and Kites
6-6 Trapezoids and Kites
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Modeling
with
Geometry
41
41.) Apply geometric methods to solve
design problems (e.g., designing an
object or structure to satisfy physical
constraints or minimize cost, working
with typographic grid systems based on
ratios).* [G-MG3]
15.) 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. [G-SRT2]
Similarity,
Right
Triangles,
and
Trigonometry
Congruence
[G-MG3]
15
[G-SRT2]
2
[G-CO2]
Congruence
10
[G-CO10]
Page 10 of 28
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). [G-CO2]
10.) Prove theorems about triangles..
[G-CO10]
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Quality Core
Prerequisites
Skill
Textbook Resources
1
4
5
7-1 Ratios and Proportions
7-7 Scale Drawings and
Models
C.1.h
3
5
7
7-2 Similar Polygons
7-3 Similar Triangles
7-6 Similarity
Transformations
G.1.e
5
6
7-6 Similarity
Transformations
C.1.e
D.2.b
D.2.j
2
3
5
VII-7
VII-3
Standards for
Mathematical
Practice
Algebra 2
PreCalculus
7-4 Parallel Lines and
Proportional Parts
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
12
12.) Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software.. [G-CO12]
16.) Use the properties of similarity
transformations to establish the angleangle (AA) criterion for two triangles to
be similar. [G-SRT3]
[G-CO12]
Similarity,
Right
Triangles,
and
Trigonometry
Similarity,
Right
Triangles,
and
Trigonometry
Similarity,
Right
Triangles,
and
Trigonometry
Page 11 of 28
16
G-SRT3]
17
[G-SRT4]
18
[G-SRT5]
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
D.1.a
D.1.c
D.1.d
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
5
6
7-4 Parallel Lines and
Proportional Parts
VII-3
C.1.h
3
7-3 Similar Triangles
7-6 Similarity
Transformations
17.) Prove theorems about triangles..
[G-SRT4]
VII-3
D.2.e
3
5
7-3 Similar Triangles
7-4 Parallel Lines and
Proportional Parts
7-5 Parts of Similar
Triangles
18.) Use congruence and similarity
criteria for triangles to solve problems
and to prove relationships in geometric
figures. [G-SRT5]
VII-3
D.2.d
E.1.e
E.1.g
3
4
6
7
7-3 Similar Triangles
7-4 Parallel Lines and
Proportional Parts
7-5 Parts of Similar
Triangles
7-6 Similarity
Transformations
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Expressing
Geometric
Properties
with
Equations
31
31.) 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). [G-GPE5]
32.) Find the point on a directed line
segment between two given points
that partitions the segment in a given
ratio. [G-GPE6]
Expressing
Geometric
Properties
with
Equations
Modeling
with
Geometry
Congruence
[G-GPE5]
32
[G-GPE6]
41
[G-MG3]
10
[G-CO10]
Similarity,
Right
Triangles,
and
Trigonometry
Page 12 of 28
17
[G-SRT4]
41.) Apply geometric methods to solve
design problems (e.g., designing an
object or structure to satisfy physical
constraints or minimize cost, working
with typographic grid systems based on
ratios).* [G-MG3]
10.) Prove theorems about triangles..
[G-CO10]
17.) Prove theorems about triangles.
[G-SRT4]
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
C.1.d
D.1.f
G.1.a
G.1.c
3
8
Algebra 2
7-3 Extend Proofs of
Perpendicular and Parallel
Lines
G.1.e
2
7
8
Algebra 2
7-4 Parallel Lines and
Proportional Parts
1
4
5
VII-2
C.1.e
D.2.b
D.2.j
D.2.e
Textbook Resources
8-2 Pythagorean Theorem
and Converse
2
3
5
Algebra 2
PreCalculus
8-2 Explore Proofs Without
Words
3
5
Algebra 2
PreCalculus
8-1 Geometric Mean
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Similarity,
Right
Triangles,
and
Trigonometry
Similarity,
Right
Triangles,
and
Trigonometry
18
18.) Use congruence and similarity
criteria for triangles to solve problems
and to prove relationships in geometric
figures. [G-SRT5]
D.2.d
E.1.e
E.1.g
3
4
6
7
8-1 Geometric Mean
19.) 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. [G-SRT6]
H.1.b
2
6
7
8
8-3 Special Right Triangles
8-4 Explore Trigonometry
8-4 Extend Secant,
Cosecant, Cotangent
8-4 Trigonometry
20.) Explain and use the relationship
between the sine and cosine of
complementary angles. [G-SRT7]
H.1.b
2
3
Algebra 2
8-4 Trigonometry
D.2.e
H.1.a
H.1.b
H.1.c
1
4
5
Algebra 2
8-2 Pythagorean Theorem
and Converse
8-4 Trigonometry
8-5 Angles of Elevation and
Depression
8-6 Law of Sines and Law of
Cosines
Similarity,
Right
Triangles,
and
Trigonometry
Similarity,
Right
Triangles,
and
Trigonometry
Page 13 of 28
[G-SRT5]
19
[G-SRT6]
20
[G-SRT7]
21
[G-SRT8]
21.) Use trigonometric ratios and the
Pythagorean Theorem to solve right
triangles in applied problems.* [GSRT8]
VII-2
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Similarity,
Right
Triangles,
and
Trigonometry
Similarity,
Right
Triangles,
and
Trigonometry
Expressing
Geometric
Properties
with
Equations
Congruence
22
22.) (+) Prove the Law of Sines and the
Law of Cosines and use them to solve
problems. [G-SRT10]
[G-SRT10]
23
[G-SRT11]
32
[G-GPE6]
2
[G-CO2]
Page 14 of 28
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
D.2.f
1
4
Algebra 2
PreCalculus
8-6 Law of Sines and Law of
Cosines
23.) (+) 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). [G-SRT11]
D.2.f
1
4
Algebra 2
PreCalculus
8-6 Extend Ambiguous Case
8-6 Law of Sines and Law of
Cosines
32.) Find the point on a directed line
segment between two given points
that partitions the segment in a given
ratio. [G-GPE6]
G.1.c
2
7
8
Algebra 2
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).
[G-CO2]
G.1.e
5
6
8-7 Vectors
9-1 Reflections
9-2 Translations
9-3 Explore Rotations
9-3 Rotations
9-4 Explore Compositions
of Transformations
9-4 Compositions of
Transformations
9-6 Dilations
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
3
3.) Given a rectangle, parallelogram,
trapezoid, or regular polygon, describe
the rotations and reflections that carry
it onto itself. [G-CO3]
4.) Develop definitions of rotations,
reflections, and translations in terms of
angles, circles, perpendicular lines,
parallel lines, and line segments. [GCO4]
[G-CO3]
Congruence
4
[G-CO4]
Congruence
5
[G-CO5]
Page 15 of 28
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. [G-CO5]
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
3
5
7
9-5 Symmetry
C.1.a
E.1.e
5
6
7
9-1 Reflections
9-2 Translations
9-3 Rotations
9-4 Explore Compositions
of Transformations
9-4 Compositions of
Transformations
E.1.a
E.1.e
3
5
7
9-1 Reflections
9-2 Translations
9-3 Explore Rotations
9-3 Rotations
9-4 Explore Compositions
of Transformations
9-4 Compositions of
Transformations
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
6
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. [G-CO6]
E.1.a
3
5
7
9-1 Reflections
9-2 Translations
9-3 Rotations
9-4 Compositions of
Transformations
9-6 Explore Dilations
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. [G-CO7]
C.1.g
E.1.b
3
9-1 Reflections
9-2 Translations
9-3 Rotations
9-4 Compositions of
Transformations
9-6 Extend Establishing
Triangle Congruence and
Similarity
8.) Explain how the criteria for triangle
congruence, angle-side-angle (ASA),
side-angle-side (SAS), and side-sideside (SSS), follow from the definition of
congruence in terms of rigid motions.
[G-CO8]
C.1.f
2
3
9-6 Extend Establishing
Triangle Congruence and
Similarity
[G-CO6]
Congruence
7
[G-CO7]
Congruence
8
[G-CO8]
Page 16 of 28
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
12
12.) Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software. [G-CO12]
[G-CO12]
Similarity,
Right
Triangles,
and
Trigonometry
Similarity,
Right
Triangles,
and
Trigonometry
Page 17 of 28
14a
[G-SRT1a]
14b
. [G-SRT1b]
14.) Verify experimentally the
properties of dilations given by a
center and a scale factor. [G-SRT1]
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. [GSRT1a]
14.) Verify experimentally the
properties of dilations given by a
center and a scale factor. [G-SRT1]
b. The dilation of a line segment is
longer or shorter in the ratio given by
the scale factor. [G-SRT1b]
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
D.1.a
D.1.c
D.1.d
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
5
6
9-1 Reflections
9-3 Explore Rotations
9-5 Extend Exploring
Constructions with a
Reflective Device
2
5
6
8
9-6 Explore Dilations
9-6 Dilations
2
5
6
8
9-6 Explore Dilations
9-6 Dilations
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Similarity,
Right
Triangles,
and
Trigonometry
15
15.) 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. [G-SRT2]
16.) Use the properties of similarity
transformations to establish the angleangle (AA) criterion for two triangles to
be similar. [G-SRT3]
Similarity,
Right
Triangles,
and
Trigonometry
Page 18 of 28
. [G-SRT2]
16
[G-SRT3]
3rd 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
C.1.h
E.1.c
E.1.d
3
5
7
9-6 Extend Establishing
Triangle Congruence and
Similarity
C.1.h
3
9-6 Extend Establishing
Triangle Congruence and
Similarity
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Congruence
1
[G-CO1]
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. [G-CO1]
Congruence
12
[G-CO12]
12.) Make formal geometric constructions
with a variety of tools and methods such as
compass and straightedge, string, reflective
devices, paper folding, and dynamic geometric
software.. [G-CO12]
Congruence
13
[G-CO13]
13.) Construct an equilateral triangle, a
square, and a regular hexagon inscribed in a
circle. [G-CO13]
Circles
24
[G-C1]
24.) Prove that all circles are similar. [G-C1]
Page 19 of 28
IV-1
IV-1
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
C.1.a
6
10-1 Circles and
Circumference
D.1.a
D.1.c
D.1.d
5
6
10-3 Arcs and Chords
10-5 Extend Inscribed
and Circumscribed
Circles
10-5 Tangents
5
6
10-5 Extend Inscribed
and Circumscribed
Circles
3
5
Algebra 2
PreCalculus
10-1 Circles and
Circumference
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
Circles
25
[G-C2]
25.) Identify and describe relationships among
inscribed angles, radii, and chords [G-C2]
D.3.a
D.3.b
D.3.c
1
3
5
PreCalculus
10-1Circles and
Circumference
10-2 Measuring Angles
and Arcs
10-3 Arcs and Chords
10-4 Inscribed Angles
10-5 Tangents
Circles
26
[G-C3]
26.) Construct the inscribed and circumscribed
circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
[G-C3]
D.2.b
D.3.d
3
5
10-4 Inscribed Angles
10-5 Extend Inscribed
and Circumscribed
Circles
Circles
27
[G-C4]
27.) (+) Construct a tangent line from a point
outside a given circle to the circle. [G-C4]
D.3.c
1
2
10-5 Tangents
Circles
28
[G-C5]
F.1.d
F.1.e
2
3
6
7
10-2 Measuring Angles
and Arcs
Expressing
Geometric
Properties
with
Equations
29
[G-GPE1]
28.) 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. [G-C5]
29.) 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. [G-GPE1]
G.1.d
D.1.e
2
3
7
8
10-8 Equations of
Circles
Page 20 of 28
IV-1
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Expressing
Geometric
Properties
with
Equations
Expressing
Geometric
Properties
with
Equations
Geometric
Measurement
and
Dimension
30
[G-GPE4]
30.) Use coordinates to prove simple
geometric theorems algebraically. [G-GPE4]
32
[G-GPE6]
32.) Find the point on a directed line segment
between two given points that partitions the
segment in a given ratio. [G-GPE6]
35
[G-GMD1]
35.) Give an informal argument for the
formulas for the circumference of a circle;
area of a circle; and volume of a cylinder,
pyramid, and cone.. [G-GMD1]
Modeling
with
Geometry
41
[G-MG3]
41.) Apply geometric methods to solve design
problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost, working with typographic grid
systems based on ratios).* [G-MG3]
Expressing
Geometric
Properties
with
Equations
33
[G-GPE7]
33.) Use coordinates to compute perimeters
of polygons and areas of triangles and
rectangles, e.g., using the distance formula.*
[G-GPE7]
Page 21 of 28
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
IV-1
IV-1
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
G.1.b
G.1.c
2
3
7
Algebra 2
10-8 Equations of
Circles
G.1.c
2
7
8
Algebra 2
10-8 Equations of
Circles
D.4.a
F.2.a
F.2.b
E.1.f
E.1.h
3
4
5
10-1 Circles and
Circumference
1
4
5
10-3 Arcs and Chords
1
2
5
6
11-1 Areas of
Parallelograms and
Triangles
F.2.a
G.1.c
Textbook Resources
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Modeling
with
Geometry
40
[G-MG2]
Modeling
with
Geometry
41
[G-MG3]
Circles
28
[G-C5]
40.) Apply concepts of density based on area
and volume in modeling situations (e.g.,
persons per square mile, British Thermal Units
(BTUs) per cubic foot).* [G-MG2]
41.) Apply geometric methods to solve design
problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost, working with typographic grid
systems based on ratios).* [G-MG3]
28.) 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. [G-C5]
Geometric
Measurement
and
Dimension
35
[G-GMD1]
Page 22 of 28
35.) Give an informal argument for the
formulas for the circumference of a circle;
area of a circle; and volume of a cylinder,
pyramid, and cone. Use dissection arguments,
Cavalieri's principle, and informal limit
arguments. [G-GMD1]
IV-1
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
1
4
5
11-2 Extend Population
Density
1
4
5
11-2 Areas of
Trapezoids, Rhombi,
Kites
11-3 Areas of Circles
and Sectors
IV-1
F.1.d
F.1.e
2
3
6
7
IV-1
D.4.a
F.2.a
F.2.b
E.1.f
E.1.h
3
4
5
Algebra 2
PreCalculus
11-3 Areas of Circles
and Sectors
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Expressing
Geometric
Properties
with
Equations
34
(Alabama)
34.) Determine areas and perimeters of
regular polygons, including inscribed or
circumscribed polygons, given the coordinates
of vertices or other characteristics. (Alabama)
Modeling
with
Geometry
41
[G-MG3]
Modeling
with
Geometry
39
[G-MG1]
Geometric
Measurement
and
Dimension
35
[G-GMD1]
41.) Apply geometric methods to solve design
problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost, working with typographic grid
systems based on ratios).* [G-MG3]
39.) Use geometric shapes, their measures,
and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a
cylinder).* [G-MG1]
35.) Give an informal argument for the
formulas for the circumference of a circle;
area of a circle; and volume of a cylinder,
pyramid, and cone. Use dissection arguments,
Cavalieri's principle, and informal limit
arguments. [G-GMD1]
Page 23 of 28
G.1.c
IV-1
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
11-4 Explore
Investigating Areas of
Regular Polygons
11-4 Extend Regular
Polygons on the
Coordinate Plane
11-4 Areas of Regular
Polygons and
Composite Figures
11-4 Areas of Regular
Polygons and
Composite Figures
1
6
1
4
5
IV-1,
VII-3
D.1.a
E.1.h
4
5
7
IV-1
D.4.a
F.2.a
F.2.b
E.1.f
E.1.h
3
4
5
Textbook Resources
11-5 Areas of Similar
Figures
Algebra 2
PreCalculus
12-4 Volumes of Prisms
and Cylinders
12-5 Volume of
Pyramids and Cones
12-6 Surface Areas and
Volumes of Spheres
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Geometric
Measurement
and
Dimension
36
[G-GMD3]
36.) Use volume formulas for cylinders,
pyramids, cones, and spheres to solve
problems.* [G-GMD3]
Geometric
Measurement
and
Dimension
Geometric
Measurement
and
Dimension
37
(Alabama)
38
[G-GMD4]
Modeling
with
Geometry
39
[G-MG1]
Page 24 of 28
Content Standard Description
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
IV-1
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
D.4.a
F.2.a
F.2.c
1
2
3
4
5
12-4 Volumes of Prisms
and Cylinders
12-5 Volumes of
Pyramids and Cones
12-6 Surface Area and
Volumes of Spheres
37.) Determine the relationship between
surface areas of similar figures and volumes of
similar figures. (Alabama)
D.4.a
F.2.a
F.2.c
1
6
12-8 Congruent and
Similar Solids
38.) Identify the shapes of two-dimensional
cross-sections of three-dimensional objects,
and identify three-dimensional objects
generated by rotations of two-dimensional
objects. [G-GMD4]
39.) Use geometric shapes, their measures,
and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a
cylinder).* [G-MG1]
D.4.b
4
5
7
12-1 Representations
of 3-D Figures
D.1.a
E.1.h
4
5
7
12-3 Surface Areas of
Pyramids and Cones
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
Domain
Content
Standard #
and
Identifier
Content Standard Description
Modeling
with
Geometry
40
[G-MG2]
40.) Apply concepts of density based on area
and volume in modeling situations (e.g.,
persons per square mile, British Thermal Units
(BTUs) per cubic foot).* [G-MG2]
1
4
5
12-4 Volumes of Prisms
and Cylinders
12-5 Volumes of
Pyramids and Cones
Modeling
with
Geometry
41
[G-MG3]
41.) Apply geometric methods to solve design
problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost, working with typographic grid
systems based on ratios).* [G-MG3]
1
4
5
12-2 Surface Areas of
Prisms and Cylinders
Modeling
with
Geometry
41
[G-MG3]
1
4
5
13-4 Simulations
Using
Probability to
Make
Decisions
42
[S-MD6]
41.) Apply geometric methods to solve design
problems (e.g., designing an object or
structure to satisfy physical constraints or
minimize cost, working with typographic grid
systems based on ratios).* [G-MG3]
42.) (+) Use probabilities to make fair
decisions (e.g., drawing by lots, using a
random number generator). [S-MD6]
1
4
5
13-4 Simulations
Page 25 of 28
F.1.c
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook Resources
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Domain
Content
Standard #
and
Identifier
Content Standard Description
Using
Probability to
Make
Decisions
43
[S-MD7]
43.) (+) Analyze decisions and strategies using
probability concepts (e.g. product testing,
medical testing, pulling a hockey goalie at the
end of a game). [S-MD7]
Page 26 of 28
4th 9 Weeks
AHSGE ACT/Quality
Core
Standards
Description
VII-6
F.1.c
Standards for
Mathematical
Practice
1
2
4
Quality Core
Prerequisites
Skill
Textbook Resources
13-3 Geometric
Probability
13-5 Probabilities of
Independent and
Dependent Events
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Essential Vocabulary
st
nd
1 9 Weeks
2 9 Weeks
Chapter 1
acute angle, adjacent angles, angle, angle
bisector, area, base, between,
circumference, collinear, complementary
angles, concave, cone, congruent,
construction, convex, coplanar, cylinder,
degree, distance, edge, equiangular
polygon, equilateral polygon, exterior,
face, interior, intersection, line, line
segment, linear pair, midpoint, n-gon,
obtuse angle, opposite rays, perimeter,
perpendicular, plane, Platonic solid,
point, polygon, polyhedron, prism,
pyramid, ray, regular polygon, regular
polyhedron, right angle, segment
bisector, side, space, sphere,
supplementary angles, surface area,
undefined term, vertex, vertex of a
polygon, vertical angles, volume
Chapter 4
acute triangle, auxiliary line, base angles,
congruence transformation, congruent
polygons, coordinate proof, corollary,
corresponding parts, equiangular
triangular, equilateral triangle, exterior
angle, flow proof, included angle,
included side, isosceles triangle, obtuse
triangle, reflection, remote interior
angles, right triangle, rotation, scalene
triangle, rotation, scalene triangle,
translation, vertex angle
Chapter 2
algebraic proof, axiom, compound
statement, conclusion, conditional
statement, conjecture, contra-positive,
converse, counterexample, deductive
argument, deductive reasoning,
disjunction, formal proof, hypothesis, ifthen statement, inductive reasoning,
informal proof, inverse, logically
equivalent, negation, paragraph proof,
postulate, proof, related conditionals,
statement, theorem, truth table, truth
value, two-column proof
Chapter 6
base, base angle, diagonal, isosceles
trapezoid, kite, legs, midsegment of a
trapezoid, parallelogram, rectangle,
rhombus, square, trapezoid
Page 27 of 28
Chapter 5
altitude, centroid, circumcenter,
concurrent lines, incenter, indirect proof,
indirect reasoning, median, orthocenter,
perpendicular bisector, point of
concurrency, proof by contradiction
3rd 9 Weeks
Chapter 7
cross products, dilation, enlargement,
extremes, means, midsegment of a
triangle, proportion, ratio, reduction,
scale, scale drawing, scale factor, scale
model, similar polygons, similarity
transformation
Chapter 8
angle of depression, angle of elevation,
component form, cosine, direction,
geometric mean, inverse cosine, inverse
sine, inverse tangent, Law of Cosines,
Law of Sines, magnitude, Pythagorean
triple, resultant, sine, standard position,
tangent, trigonometric ratio,
trigonometry, vector
Chapter 9
angle of rotation, axis symmetry, center
of rotation, composition of
transformations, glide reflection, line of
reflection, line of symmetry, line
symmetry, magnitude of symmetry,
order of symmetry, plane symmetry,
rotational symmetry, symmetry,
translation vector
4th 9 Weeks
Chapter 10
adjacent arcs, arc, arc length, center, central
angle, chord, chord segment, circle,
circumference, circumscribed, common
tangent, compound locus concentric circles,
congruent arcs, diameter, external secant
segment, inscribed, inscribed angle,
intercepted arc, major arc, minor arc, pi,
point of tangency, radius, secant, secant
segment, semicircle, tangent
Chapter 11
apothem, base of a parallelogram, base of a
triangle, center of a regular polygon, central
angle of a regular polygon, composite figure,
height of a parallelogram, height of a
trapezoid, height of a triangle, radius of a
regular polygon, sector of a circle
Chapter 12
altitude, axis, base edges, composite solid,
congruent solid, cross section, Euclidean
geometry, great circle, isometric view, lateral
area, lateral edge, lateral face, non-Euclidean
geometry, oblique cone, oblique solid,
regular pyramid, right cone, right solid,
similar solids, slant height, spherical
geometry, topographic map
Chapter 13
circular permutation, combination,
complement, compound events, conditional
probability, dependent events, expected
value, factorial, Fundamental Counting
Principle, geometric probability, independent
events, mutually exclusive events,
permutation, probability model, probability
tree, random variable, sample space,
simulation, tree diagram
BCSS Mathematics Pacing Guide 2013 - 2014
Geometry
Essential Vocabulary
st
1 9 Weeks
Chapter 3
alternate exterior angles, alternate
interior angles, consecutive interior
angles, corresponding angles,
equidistant, parallel lines, parallel planes,
point-slope form, rate of change, skew
lines, slope, slope-intercept form,
transversal
Page 28 of 28
nd
2 9 Weeks
3rd 9 Weeks
4th 9 Weeks