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Tallapoosa County
Mathematics Guide
Advanced Geometry
The objectives to be covered are listed by 9-weeks and should be covered during the four grading
periods. You are also provided with a suggested sequencing of the objectives per term but you
may choose to reorder them as long as you cover the stated objectives during the indicated
quarter. The benchmark tests that will be administered at the end of each 9-weeks grading
period will reflect the objectives listed for each term.
TEXTBOOK: Glencoe – Geometry incorporating the IMP units: “Shadows” and “Bees Do It
Best” whenever possible. Refer to the TEAM-Math Curriculum Guide for the incorporation of
the IMP units.
1st 9-Weeks
2nd 9-Weeks
3rd 9-Weeks
4th 9-weeks
COS #1, #2, #9, #11, #12, #17
COS #3, #5, #6, #7, #8, #9, #10
COS #3, #4, #5, #13, #15, #18
COS #11, #14, #15, #16, #17
SUGGESTED PACING GUIDE
Approximate time frame for instruction:
Begin 1st 9-weeks grading period.
Chapter 1: Sections 1-6
Chapter 2: Sections 1-8
Chapter 3: Sections 1-5
End 1st 9-weeks grading period.
2.5 weeks
3 weeks
2.5 weeks
Begin 2nd 9-weeks grading period.
Chapter 4: Sections 1-6
Chapter 5: Sections 1-2, 4-5
Chapter 6: Sections 1-5
Chapter 7: Sections 1-5
End 2nd 9-weeks grading period.
2.5 weeks
2.0 weeks
2.0 weeks
1.5 weeks
Begin 3rd 9-weeks grading period.
Chapter 8: Sections 1-7
Chapter 9: Sections 1- 3, & 6
Chapter 10: Sections 1-8
*Exit Exam review & testing
End 3rd 9-weeks grading period.
2.5 weeks
1.5 weeks
2.5 weeks
1.5 weeks
Begin 4th 9-weeks grading period
Chapter 11: Sections 1-5
Chapter 12: Sections 1-7
Chapter 13: Sections 1-4
th
End 4 9-weeks grading period
2 weeks
3 weeks
2.5 weeks
Chapter(s) 1, 2 & 3
Chapter(s) 4, 5, 6, & 7
Chapter(s) 8, 9 & 10
Chapter(s) 11, 12, & 13
Tallapoosa County Sequencing Guide
Advanced Geometry
1st 9-Weeks
UNIT 1: Fundamentals of Geometry – Lines, Angle, and Logic - Chapters 1, 2 & 3
TOPIC:
1) Understand undefined terms of geometry – point, line, plane (Chapter 1: Section 1)
2) Demonstrate competency with measurement tools – ruler, protractor, compass
(Chapter 1: Section 2)
3) Apply distance, midpoint, and slope formulas connecting to the Pythagorean
Theorem (Chapter 1: Section 3)
4) Identify angle relationships and justify theorems related to pairs of angles
(Chapter 1: Sections 4 & 5)
5) Introduction to coordinate geometry through perimeter of polygons (Chapter 1:
Section 6)
6) Use inductive and deductive reasoning to analyze information (Chapter 2:
Sections 1-4)
7) Using methods of proof to justify theorems and to analyze information(Chapter 2:
Sections 5-8)
8) Determine equations of parallel and perpendicular lines (Chapter 3: Sections 1-5)
9) Apply equations to geometric problems (Chapter 3)
COS #1: Determine the equation of a line parallel or perpendicular to a
second line through a given point.
COS #2: Justify theorems related to pairs of angles, including angles
formed by parallel and perpendicular lines, vertical angles, adjacent angles,
complementary angles, and supplementary angles.
COS #9: Use inductive reasoning to make conjectures and deductive
reasoning to justify conclusions.
 Recognizing the limitations of justifying a conclusion through
inductive reasoning
COS # 11: Determine the areas and perimeters of regular polygons, including
inscribed or circumscribed polygons, given the coordinates of vertices or
other characteristics.
COS #12: Apply distance, midpoint, and slope formulas to solve problems
and to confirm properties of polygons.
Examples: finding the area of a rectangle given the coordinates of its
vertices, showing that the median of a trapezoid is half the sum of the
bases.
COS #17: Analyze sets of data from geometric contexts to determine what, if
any, relationships exist.
Example: Collect data and create a scatterplot comparing the perimeter
and area of various rectangles. Determine whether a line of best fit can be
drawn.
 Distinguishing between conclusions drawn when using deductive
and statistical reasoning
Tallapoosa County Sequencing Guide
Advanced Geometry

Calculating probabilities arising in geometric contexts
Example: finding the probability of hitting a particular ring on a
dart board whose rings are formed by equally spaced concentric
circles
2nd 9-Weeks
UNIT 2: Triangles – Classification, Congruency, Similarity, and Trigonometry –
Chapters 4, 5, 6, & 7
TOPIC:
1) Classify types of triangles (Chapter 4: Section 1)
2) Apply angle properties of triangles (Chapter 4: Section 2)
3) Prove triangles are congruent and us properties of congruency to find missing
measures (CPCTC) (Chapter 4: Sections 3, 4, & 5)
4) Utilize the properties of isosceles and equilateral triangles to determine missing
measures (Chapter 4: Section 6)
5) Identify special segments of triangles, their intersections and their measurement
properties (Chapter 5: Section 1)
6) Apply triangle inequalities and other inequalities to geometric problems
(Chapter 5: Sections 2, 4, & 5)
7) Apply properties of similar triangles including use of scale factors and
proportions (Chapter 6: Sections 1-5)
8) Determine geometric mean to fins missing lengths in right triangles (Chapter 7:
Section 1)
9) Apply Pythagorean theorem, special right triangle rules, and other operations
involving radicals to find missing lengths of sides (Chapter 7: Sections 2 & 3)
10) Apply right triangle definitions of sine, cosine and tangent to find missing
measures (Chapter 7: Sections 4 & 5)
11) Apply factoring and use of polynomials in problem solving applications
(Chapters 4-7)
COS #3: Verify the relationships among different classes of polygons by
using their properties
Example: showing that a square has all the properties of both a rectangle
and a rhombus
 Determining the missing lengths of sides or measures of angles in
similar polygons
COS #5: Solve real-life and mathematical problems using properties and
theorems related to circles, quadrilaterals, and other geometric shapes.
Example: finding the center of a solid wooden wheel using the
perpendicular bisectors of two chords
 Determining the equation of a circle given its center and radius
COS #6: Apply the Pythagorean Theorem to solve application problems,
expressing answers in simplified radical form or as decimal approximations,
using Pythagorean triples when applicable.
Tallapoosa County Sequencing Guide
Advanced Geometry
COS #7: Use the ratios of the sides of special right triangles to find lengths of
missing sides.
 Deriving the ratios of the sides of 30-60-90 and 45-45-90
triangles
COS #8: Deduce relationships between two triangles, including proving
congruence or similarity of the triangles from given information, using the
relationships to solve problems and to establish other relationships.
 Determining the geometric mean to find missing lengths in right
triangles
COS #9: Use inductive reasoning to make conjectures and deductive
reasoning to justify conclusions.
 Recognizing the limitations of justifying a conclusion through
inductive reasoning
COS #10: Find the missing measures of sides and angles in right triangles by
applying the right triangle definitions of sine, cosine, and tangent.
3rd 9-Weeks
UNIT 3: Geometric Figures – Quadrilaterals, Transformations and Circles
(Chapters 8 & 9)
TOPIC:
1) Determine the measures of interior and exterior angles associated with polygons
and verify the formulas (Chapter 8: Section 1)
2) Identify quadrilaterals from verbal descriptions of properties and apply the
properties of these quadrilaterals (Chapter 8: Sections 2 – 6)
3) Understand and analyze properties of transformations and apply the coordinate
geometry of transformations (Chapter 8: Section 7 and Chapter 9: Sections 1-3)
4) Introduce operations with vectors (Chapter 9: Section 6)
5) Understand and apply properties of circles including arcs, chords, secants,
tangents, and angles related to circles (Chapter 10: Sections 1-7)
6) Real life applications related to circles, quadrilaterals and other geometric shapes
(Chapters 8, 9 & 10)
7) Construct with precision a circle graph representing given data (Chapter 10:
Section 2)
8) Determine the equation of a circle (Chapter 10: Section 8)
COS #3: Verify the relationships among different classes of polygons by
using their properties.
Example: showing that a square has all the properties of both a rectangle
and a rhombus
 Determining the missing lengths of sides or measures of angles in
similar polygons
COS #4: Determine the measure of interior and exterior angles associated
with polygons.
Tallapoosa County Sequencing Guide
Advanced Geometry

Verifying the formulas for the measures of interior and exterior
angles of polygons inductively and deductively
COS #5: Solve real-life and mathematical problems using properties and
theorems related to circles, quadrilaterals, and other geometric shapes.
Example: finding the center of a solid wooden wheel using the
perpendicular bisectors of two chords
 Determining the equation of a circle given its center and radius
COS #13: Identify the coordinates of the vertices of the image of a given
polygon that is translated, rotated, reflected, or dilated.
Example: rotating a triangle a given number of degrees around a specific
point, comparing the vertices of the image and preimage
COS #15: Calculate measures of arcs and sectors of a circle from given
information.
Examples: finding the area of a sector given its arc length and radius,
finding the arc length of a sector given its area and radius, finding the area
or arc length given the measure of the central angle and the radius
COS #18: Construct with precision a circle graph to represent data from
given tables or classroom experiments.
4th 9-Weeks
UNIT 4: Area and Volume – Area of Polygons and Circles, Surface Area and
Volume of 3-D Figures (Chapters 11, 12, & 13)
TOPIC:
Area of polygons, circles and irregular figures (Chapter 11: Sections 1 – 4)
Calculate measures of sectors of a circle (Chapter 11: Section 5)
Calculate probabilities arising in geometric contexts (Chapter 11: Section 5)
Classify polyhedra according to their properties (Chapter 12: Section 1)
Surface Area of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop
formulas, calculate values, find missing dimensions (Chapter 12: Section 3 – 7)
6) Volume of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop
formulas, calculate values, find missing dimensions (Chapter 13: Section 1 – 3)
7) Determine relationships between surface area and volume of similar figures
(Chapter 13: Section 4)
8) Apply geometric properties and relationships in solving multi-step problems in
two and three dimensions (Chapters 11, 12, & 13)
1)
2)
3)
4)
5)
COS #11: Determine the areas and perimeters of regular polygons, including
inscribed or circumscribed polygons, given the coordinates of vertices or
other characteristics.
COS #14: Classify polyhedrons according to their properties, including the
number of faces.
Example: identifying a polyhedron having 6 vertices and 12 edges
 Identifying Euclidean solids
Tallapoosa County Sequencing Guide
Advanced Geometry
COS #15: Calculate measures of arcs and sectors of a circle from given
information.
Examples: finding the area of a sector given its arc length and radius,
finding the arc length of a sector given its area and radius, finding the area
or arc length given the measure of the central angle and the radius
COS #16: Calculate surface areas and volumes of solid figures, including
spheres, cones, and pyramids.
 Developing formulas for surface area and volume of spheres,
cones, and pyramids
 Calculating specific missing dimensions of solid figures from
surface area or volume
 Determining the relationship between the surface areas of similar
figures and volumes of similar figures
COS #17: Analyze sets of data from geometric contexts to determine what, if
any, relationships exist.
Example: Collect data and create a scatterplot comparing the perimeter
and area of various rectangles. Determine whether a line of best fit can be
drawn.
 Distinguishing between conclusions drawn when using deductive
and statistical reasoning
 Calculating probabilities arising in geometric contexts
Example: finding the probability of hitting a particular ring on a
dart board whose rings are formed by equally spaced concentric
circles
Tallapoosa County
Mathematics Guide
Geometry Concepts & Applications
The objectives to be covered are listed by 9-weeks and should be covered during the four grading
periods. You are also provided with a suggested sequencing of the objectives per term but you
may choose to reorder them as long as you cover the stated objectives during the indicated
quarter. The benchmark tests that will be administered at the end of each 9-weeks grading
period will reflect the objectives listed for each term.
TEXTBOOK: Glencoe – Geometry (Incorporate the IMP units: “Shadows” and “Bees Do It
Best” whenever possible. Refer to the TEAM-Math Curriculum Guide for the incorporation of
the IMP units.)
1st 9-Weeks
COS #1, #2, #9, #11, #12, #17
Chapter(s) 1, 2, 3, 4, 6 & 15
nd
2 9-Weeks
COS #3, #5, #6, #7, #8, #9, #10
Chapter(s) 5, 6, 7, 9, 13
rd
3 9-Weeks
COS #3, #4, #5, #13, #15, #18
Chapter(s) 8, 10, 11, 14, 16
th
4 9-weeks
COS #11, #14, #15, #16, #17
Chapter(s) 11, 12, & 15
SUGGESTED PACING GUIDE
Approximate time frame for instruction:
Begin 1st 9-weeks grading period.
Chapter 1: Sections 1-5
Chapter 2: Sections 1-5
Chapter 6: Sections 6-7
Chapter 3: Sections 1-7
Chapter 4: Sections 1-6
Chapter 15: Sections 1-5
st
End 1 9-weeks grading period.
Begin 2nd 9-weeks grading period.
Chapter 5: Sections 1-6
Chapter 6: Sections 1-5
Chapter 7: Sections 1-4
Chapter 9: Sections 1-7
Chapter 13: Sections 1-5
nd
End 2 9-weeks grading period.
Begin 3rd 9-weeks grading period.
Chapter 8: Sections 1-5
Chapter 16: Sections 3-6
Chapter 10: Sections 1-2
Chapter 11: Sections 1-3
Chapter 14: Sections 1-5
End 3rd 9-weeks grading period.
Begin 4th 9-weeks grading period
Chapter 11: Sections 4-6
Chapter 12: Sections 1-7
Chapter 15: Section 6
Chapter 16: Sections 1-2
th
End 4 9-weeks grading period
1.5 weeks
1 week
.5 week (in conjunction with chapter 2)
2 weeks
1.5 weeks
1.5 weeks
2 weeks
1.5 weeks
1 week
1.5 weeks
2 weeks
1.5 weeks
1 week (in conjunction with Chapter 8)
.5 week (in conjunction with Chapter 8)
1.5 weeks
2 weeks
1 week
3 weeks
1 week
1 week
Tallapoosa County Sequencing Guide
Geometry: Concepts and Applications
1st 9-Weeks
UNIT 1: Fundamentals of Geometry – Lines, Angle, and Logic - Chapters
1, 2, 3, 4, 6 & 15
TOPIC:
1) Use inductive and deductive reasoning to analyze information (Chapter 1:
Sections 1, 4)
2) Understand undefined terms of geometry – point, line, plane (Chapter 1:
Sections 2-3)
3) Demonstrate competency with measurement tools – ruler, protractor,
compass (Chapter 1: Section 5)
4) Apply distance, midpoint, and slope formulas connecting to the Pythagorean
Theorem (Chapter 2: Sections 1-5; Chapter 6: Sections 6-7 )
5) Identify angle relationships and justify theorems related to pairs of angles
(Chapter 3: Sections 1-6, Chapter 4: Sections 1-4)
6) Introduction to coordinate geometry through perimeter of polygons (Chapter
1: Section 6)
7) Using methods of proof to justify theorems and to analyze information
(Chapter 1: Sections 1-6, Chapter 15: Sections 1-5)
8) Determine equations of parallel and perpendicular lines (Chapter 3: Section
7, Chapter 4: Sections 5 & 6)
9) Apply equations to geometric problems (Chapter 3)
COS #1: Determine the equation of a line parallel or perpendicular to
a second line through a given point.
COS #2: Justify theorems related to pairs of angles, including angles
formed by parallel and perpendicular lines, vertical angles, adjacent
angles, complementary angles, and supplementary angles.
COS #9: Use inductive reasoning to make conjectures and deductive
reasoning to justify conclusions.
 Recognizing the limitations of justifying a conclusion
through inductive reasoning
COS # 11: Determine the areas and perimeters of regular polygons,
including inscribed or circumscribed polygons, given the coordinates
of vertices or other characteristics.
COS #12: Apply distance, midpoint, and slope formulas to solve
problems and to confirm properties of polygons.
Examples: finding the area of a rectangle given the coordinates of
its vertices, showing that the median of a trapezoid is half the sum
of the bases.
COS #17: Analyze sets of data from geometric contexts to determine
what, if any, relationships exist.
Tallapoosa County Sequencing Guide
Geometry: Concepts and Applications
Example: Collect data and create a scatterplot comparing the
perimeter and area of various rectangles. Determine whether a line
of best fit can be drawn.
 Distinguishing between conclusions drawn when using
deductive and statistical reasoning
 Calculating probabilities arising in geometric contexts
Example: finding the probability of hitting a particular
ring on a dart board whose rings are formed by equally
spaced concentric circles
2nd 9-Weeks
UNIT 2: Triangles – Classification, Congruency, Similarity, and
Trigonometry – Chapters 5, 6, 7, 9, & 13
TOPIC:
1) Classify types of triangles (Chapter 5: Section 1)
2) Apply angle properties of triangles (Chapter 5: Section 2)
3) Prove triangles are congruent and us properties of congruency to find
missing measures (CPCTC) (Chapter 5: Sections 4, 5, & 6)
4) Utilize the properties of isosceles and equilateral triangles to determine
missing measures (Chapter 6: Section 4)
5) Identify special segments of triangles, their intersections and their
measurement properties (Chapter 6: Sections 1-3)
6) Apply triangle inequalities and other inequalities to geometric problems
(Chapter 7: Sections 1-4)
7) Apply properties of similar triangles including use of scale factors and
proportions (Chapter 9: Sections 1-7)
8) Determine geometric mean to find missing lengths in right triangles
(Chapter 9: Section 2)
9) Apply Pythagorean theorem, special right triangle rules, and other
operations involving radicals to find missing lengths of sides (Chapter 6:
Sections 5 & 6; Chapter 13: Sections 2 & 3)
10) Apply right triangle definitions of sine, cosine and tangent to find missing
measures (Chapter 13: Sections 4 & 5)
11) Apply factoring and use of polynomials in problem solving applications
(Chapters 5-7 & 9)
COS #3: Verify the relationships among different classes of polygons
by using their properties
Example: showing that a square has all the properties of both a
rectangle and a rhombus
 Determining the missing lengths of sides or measures of
angles in similar polygons
COS #5: Solve real-life and mathematical problems using properties
and theorems related to circles, quadrilaterals, and other geometric
shapes.
Tallapoosa County Sequencing Guide
Geometry: Concepts and Applications
Example: finding the center of a solid wooden wheel using the
perpendicular bisectors of two chords
 Determining the equation of a circle given its center and
radius
COS #6: Apply the Pythagorean Theorem to solve application
problems, expressing answers in simplified radical form or as decimal
approximations, using Pythagorean triples when applicable.
COS #7: Use the ratios of the sides of special right triangles to find
lengths of missing sides.
 Deriving the ratios of the sides of 30-60-90 and 45-45-90
triangles
COS #8: Deduce relationships between two triangles, including
proving congruence or similarity of the triangles from given
information, using the relationships to solve problems and to establish
other relationships.
 Determining the geometric mean to find missing lengths
in right triangles
COS #9: Use inductive reasoning to make conjectures and deductive
reasoning to justify conclusions.
 Recognizing the limitations of justifying a conclusion
through inductive reasoning
COS #10: Find the missing measures of sides and angles in right
triangles by applying the right triangle definitions of sine, cosine, and
tangent.
3rd 9-Weeks
UNIT 3: Geometric Figures – Quadrilaterals, Transformations and Circles
(Chapters 8, 10, 11, 14 & 16)
TOPIC:
1) Determine the measures of interior and exterior angles associated with
polygons and verify the formulas (Chapter 8: Section 1, Chapter 10:
Sections 1-2)
2) Identify quadrilaterals from verbal descriptions of properties and apply the
properties of these quadrilaterals (Chapter 8: Sections 2 – 5)
3) Understand and analyze properties of transformations and apply the
coordinate geometry of transformations (Chapter 8, Chapter 16: Sections
3-6)
4) Understand and apply properties of circles including arcs, chords, secants,
tangents, and angles related to circles (Chapter 11: Sections 1-3, Chapter
14: Sections 1-5)
5) Real life applications related to circles, quadrilaterals and other geometric
shapes (Chapters 8, 10 & 14)
Tallapoosa County Sequencing Guide
Geometry: Concepts and Applications
6) Construct with precision a circle graph representing given data (Chapter
11 & Chapter 14)
7) Determine the equation of a circle (Chapter 14: Section 6)
COS #3: Verify the relationships among different classes of polygons
by using their properties.
Example: showing that a square has all the properties of both a
rectangle and a rhombus
 Determining the missing lengths of sides or measures of
angles in similar polygons
COS #4: Determine the measure of interior and exterior angles
associated with polygons.
 Verifying the formulas for the measures of interior and
exterior angles of polygons inductively and deductively
COS #5: Solve real-life and mathematical problems using properties
and theorems related to circles, quadrilaterals, and other geometric
shapes.
Example: finding the center of a solid wooden wheel using the
perpendicular bisectors of two chords
 Determining the equation of a circle given its center and
radius
COS #13: Identify the coordinates of the vertices of the image of a
given polygon that is translated, rotated, reflected, or dilated.
Example: rotating a triangle a given number of degrees around a
specific point, comparing the vertices of the image and preimage
COS #15: Calculate measures of arcs and sectors of a circle from
given information.
Examples: finding the area of a sector given its arc length and
radius, finding the arc length of a sector given its area and radius,
finding the area or arc length given the measure of the central
angle and the radius
COS #18: Construct with precision a circle graph to represent data
from given tables or classroom experiments.
4th 9-Weeks
UNIT 4: Area and Volume – Area of Polygons and Circles, Surface Area
and Volume of 3-D Figures (Chapters 11, 12, & 15)
TOPIC:
1) Area of polygons, circles and irregular figures (Chapter 11: Sections 5 &
6, Chapter 12: Section 1)
2) Calculate measures of sectors of a circle (Chapter 11: Section 6)
3) Calculate probabilities arising in geometric contexts (Chapter 15: Sections
1-2)
Tallapoosa County Sequencing Guide
Geometry: Concepts and Applications
4) Classify polyhedra according to their properties (Chapter 12: Section 1)
5) Surface Area of Solid Figures (Cylinders, Spheres, Cones, Pyramids):
develop formulas, calculate values, find missing dimensions (Chapter 12:
Section 2, 4, 6)
6) Volume of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop
formulas, calculate values, find missing dimensions (Chapter 12: Section
3, 5, 6)
7) Determine relationships between surface area and volume of similar
figures (Chapter 12: Section 7)
8) Apply geometric properties and relationships in solving multi-step
problems in two and three dimensions (Chapters 11, 12, & 15)
COS #11: Determine the areas and perimeters of regular polygons,
including inscribed or circumscribed polygons, given the coordinates
of vertices or other characteristics.
COS #14: Classify polyhedrons according to their properties,
including the number of faces.
Example: identifying a polyhedron having 6 vertices and 12 edges
 Identifying Euclidean solids
COS #15: Calculate measures of arcs and sectors of a circle from
given information.
Examples: finding the area of a sector given its arc length and
radius, finding the arc length of a sector given its area and radius,
finding the area or arc length given the measure of the central
angle and the radius
COS #16: Calculate surface areas and volumes of solid figures,
including spheres, cones, and pyramids.
 Developing formulas for surface area and volume of
spheres, cones, and pyramids
 Calculating specific missing dimensions of solid figures
from surface area or volume
 Determining the relationship between the surface areas of
similar figures and volumes of similar figures
COS #17: Analyze sets of data from geometric contexts to determine
what, if any, relationships exist.
Example: Collect data and create a scatterplot comparing the
perimeter and area of various rectangles. Determine whether a line
of best fit can be drawn.
 Distinguishing between conclusions drawn when using
deductive and statistical reasoning
 Calculating probabilities arising in geometric contexts
Example: finding the probability of hitting a particular
ring on a dart board whose rings are formed by equally
spaced concentric circles.