Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Standard 2.0
Knowledge of Geometry
A1 Analyze
properties of plane geometric figures
Grades
3 & 5 ·
Identify polygons within a composite figure Grades
5 & 6 ·
Identify and describe relationships of lines and line segments Grades
3 – 6 ·
Identify, describe, and label points, lines, rays, vertices, angles,
and planes using correct symbolic notation Grade
7 ·
Identify and describe the angles formed by intersecting lines, line
segments, and rays including vertical, adjacent, complementary, and
supplementary angles Grades
7 & 8 ·
Identify and describe the relationships between angles formed when
parallel lines are cut by a transversal including alternate interior,
alternate exterior, and corresponding angles Grades
7 & 8 ·
Identify and describe the relationship among the parts of a right
triangle A2 Analyze
geometric relationships
Grade
4 ·
Compare and classify angles in geometric figures and pictures Grade
5 ·
Compare and classify quadrilaterals by length of sides and measures
of angles Grade
6 ·
Compare and classify triangles by sides and angle measures ·
Identify and compare the relationship between parts of a circle Grades
6 & 7 ·
Determine a missing angle measure using the sum of the interior
angles of a polygon Grade
7 ·
Determine the measure of angles formed by intersecting lines, line
segments, and rays Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal B1 Analyze
the properties of solid geometric figures
Grades
3 – 5 ·
Identify and describe solid geometric figures using the number of
edges, faces, vertices, or shape of base 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.1 The student will analyze the properties of geometric figures. Assessment Limits
Ø Essential properties,
relationships, and geometric models include the following: ·
congruence and similarity ·
line/segment/plane relationships (parallel, perpendicular,
intersecting, bisecting, midpoint, median, altitude) ·
point relationships (collinear, coplanar) ·
angles and angle relationships (vertical, adjacent, complementary,
supplementary, obtuse, acute, right, interior, exterior) ·
angle relationships with parallel lines ·
polygons (regular, nonregular, composite, equilateral, equiangular) ·
geometric solids (cones, cylinders, prisms, pyramids, composite
figures) ·
circle/sphere (tangent, radius, diameter, chord, secant,
central/inscribed angle, inscribed, circumscribed). Skill Statement
The student describes and analyzes geometric figures. 
Solid
Geometric Figures
·
The student will analyze the properties and relationships of
geometric solids with bases other than rectangles, triangles, or circles. ·
The student will analyze the properties and relationships of oblique
solids. ·
The student will analyze the properties and relationships of
truncated threedimensional solids. Radians
·
The student will explore the relationship between the measure of the
central angle and the arc length in a circle. ·
The student will explore the relationship between radian measure and
the corresponding degree measure from 0 to 2π. Perspective Drawings·
The student will analyze the properties of perspective drawings
including vanishing points, lines of sight, and hidden lines. 
Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

B2 Analyze
the relationship between plane geometric figures and surfaces of solid
geometric figures Grades
3 – 5 ·
Compare plane figure to surfaces of solid geometric figures C1
Represent plane geometric figures
Objective
Grades 3 – 8 ·
Sketch or draw plane geometric figures D1 Analyze
and apply the properties of congruent and/or similar polygons
Grades
3 – 7 ·
Analyze and apply the properties of congruent polygons Grades
5 – 8 · Analyze and apply the properties of similar polygons 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.1 The student will analyze the properties of geometric figures. Assessment Limits
Ø Essential properties,
relationships, and geometric models include the following: · congruence and similarity · line/segment/plane
relationships (parallel, perpendicular, intersecting, bisecting, midpoint,
median, altitude) · point relationships
(collinear, coplanar) · angles and angle
relationships (vertical, adjacent, complementary, supplementary, obtuse,
acute, right, interior, exterior) · angle relationships with
parallel lines · polygons (regular,
nonregular, composite, equilateral, equiangular) · geometric solids (cones,
cylinders, prisms, pyramids, composite figures) · circle/sphere (tangent,
radius, diameter, chord, secant, central/inscribed angle, inscribed,
circumscribed). Skill Statement
The student describes and analyzes geometric figures. 


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will demonstrate
the ability to solve mathematical and realworld problems using measurement
and geometric models and will justify solutions and explain processes used. 
Additional Topics for a Complete Course
Would Include 

Standard 1.0 Knowledge of
Algebra, Patterns, or Functions B2 Identify, write, solve, and apply equations
and inequalities Grades
3 – 8 and Algebra/Data Analysis CLG 1.2.1 ·
Solve linear equations from onestep to variables on both sides C1 Locate points on a number line and in a
coordinate graph Grades
4 – 8 ·
Graph ordered pairs in the coordinate plane C2 Analyze linear relationships Grades 7 & 8 and Algebra/Data Analysis CLG 1.2.1 ·
Graph linear equations in a coordinate plane ·
Determine the slope of a line Standard 2.0 Knowledge of
Geometry A1 Analyze properties of plane geometric
figures Grades
3 & 5 ·
Identify polygons within a composite figure Grades
5 & 6 ·
Identify and describe relationships of lines and line segments Grades
3 – 6 ·
Identify, describe, and label points, lines, rays, vertices, angles,
and planes using correct symbolic notation Grade
7 ·
Identify and describe the angles formed by intersecting lines, line
segments, and rays including vertical, adjacent, complementary, and
supplementary angles Grades
7 & 8 ·
Identify and describe the relationships between angles formed when
parallel lines are cut by a transversal including alternate interior,
alternate exterior, and corresponding angles Grades
7 & 8 ·
Identify and describe the relationship among the parts of a right
triangle A2
Analyze geometric relationships
Grade
4 ·
Compare and classify angles in geometric figures and pictures 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.2 The student will identify and/or verify properties of geometric
figures using the coordinate plane and concepts from algebra. Assessment Limits Ø “Verify properties” means
to justify solutions using definitions and/or mathematical principles. Ø Properties, relationships,
and geometric models include the following: ·
congruence and similarity ·
line/segment relationships (parallel, perpendicular, intersecting,
bisecting, midpoint, median, altitude) ·
point relationships (collinear) ·
angles and angle relationships (obtuse, acute, right) ·
polygons (regular, nonregular, equilateral, equiangular) ·
circle (tangent, radius, diameter, chord). Ø Items for this indicator
may be set on the coordinate plane or may just have coordinates identified
with no grid. Ø Concepts from algebra
include applications of the distance, midpoint, and slope formulas. 
Polar
Coordinates *
·
The student will locate points on the polar coordinate system
including points with rotation greater than 360°. ·
The student will explore the relationship between a point on the coordinate
plane with the same point on the polar coordinate system. Threedimensional
Coordinate Plane ·
The student will represent a point in space as an ordered triple. ·
The student will use the distance and midpoint formulas for segments
in threedimensional space. ·
The student will explore relationships given a set of points in space
such as collinear, coplanar, and relative placement inside or outside a
figure. 
Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Grade
5 ·
Compare and classify quadrilaterals by length of sides and measures
of angles Grade
6 ·
Compare and classify triangles by sides and angle measures ·
Identify and compare the relationship between parts of a circle Grades
6 & 7 ·
Determine a missing angle measure using the sum of the interior
angles of a polygons Grade
7 ·
Determine the measure of angles formed by intersecting lines, line
segments, and rays Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal C1
Represent plane geometric figures
Grades
3 – 8 ·
Sketch or draw plane geometric figures Grade
6 ·
Identify, describe, or draw a polygon on a coordinate plane D1
Analyze and apply the properties of congruent and/or similar polygons
Grades 3
– 7
·
Analyze and apply the properties of congruent polygons Grades
5 – 8 ·
Analyze and apply the properties of similar polygons Standard 7.0 Processes of Mathematics B1 Justify ideas or solutions with mathematical concepts or proofs 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.2 The student will identify and/or verify properties of geometric
figures using the coordinate plane and concepts from algebra. Assessment Limits Ø “Verify properties” means
to justify solutions using definitions and/or mathematical principles. Ø Properties, relationships,
and geometric models include the following: ·
congruence and similarity ·
line/segment relationships (parallel, perpendicular, intersecting,
bisecting, midpoint, median, altitude) ·
point relationships (collinear) ·
angles and angle relationships (obtuse, acute, right) ·
polygons (regular, nonregular, equilateral, equiangular) ·
circle (tangent, radius, diameter, chord). Ø Items for this indicator
may be set on the coordinate plane or may just have coordinates identified
with no grid. Ø Concepts from algebra
include applications of the distance, midpoint, and slope formulas. 

Voluntary State Curriculum –
Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will demonstrate the ability to solve mathematical and realworld problems using measurement and geometric models and will justify solutions and explain processes used. 
Additional Topics for a Complete Course Would Include 

Standard 1.0 Knowledge of
Algebra, Patterns, or Functions C1 Locate
points on a number line and in a coordinate graph
Grades 4 – 8 ·
Graph ordered pairs in the coordinate plane Standard 2.0 Knowledge of
Geometry A1 Analyze properties of plane geometric
figures
Grades 3 & 5 ·
Identify
polygons within a composite figure Grades 5 & 6 ·
Identify and
describe relationships of lines and line segments Grades 3 – 6 ·
Identify,
describe, and label points, lines, rays, vertices, angles, and planes using
correct symbolic notation Grade 7 ·
Identify and describe
the angles formed by intersecting lines, line segments, and rays including
vertical, adjacent, complementary, and supplementary angles A2 Analyze geometric relationships
Grade 4 ·
Compare and
classify angles in geometric figures and pictures Grade 5 ·
Compare and
classify quadrilaterals by length of sides and measures of angles Grade 6 ·
Compare and
classify triangles by sides and angle measures C1 Represent plane geometric figures
Grades 3 – 8 ·
Sketch or draw
plane geometric figures Grades 7 & 8 ·
Construct
geometric figures using a variety of construction tools 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.3 The student will use transformations
to move figures, create designs, and/or demonstrate geometric properties. Assessment Limits
Ø
Transformations
include reflections, rotations, translations, and dilations. Ø
Items should go
beyond the identification of transformations. Ø
Essential
properties and relationships include the following: congruence, similarity,
and symmetry. Ø
The student’s
explanation of a transformation must include the following: ·
translation –
distance and direction ·
reflection –
line of reflection ·
rotation –
center of rotation, angle measure, direction (clockwise or counterclockwise) ·
dilation –
center and scale factor. Ø
Paper folding
and the use of Mirasä and mirrors are appropriate methods for performing transformations,
and their use must be referenced. Skill Statement
Given one or more
transformations, the student sketches the result of the transformation(s)
and/or explains the geometric effect of the transformation(s) on the figure. 
Matrices ·
The student will
write and plot ordered pairs from matrix notation. ·
The student will
find transformation images, including rotations, reflections, dilations and
translations, using matrices. Vectors ·
The student will
identify the distance and direction of a given vector. ·
The student will
find resultant vectors. ·
The student will
describe translations using vectors. ·
The student will
find translation images using vector sums. 
Voluntary State Curriculum –
Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will demonstrate the ability to solve mathematical and realworld problems using measurement and geometric models and will justify solutions and explain processes used. 
Additional Topics for a Complete Course Would Include 

D1 Analyze and apply the properties of
congruence and/or similar polygons Grades 3 – 7 ·
Analyze and
apply the properties of congruent polygons Grades 5 – 8 ·
Analyze and
apply the properties of similar polygons E1 Analyze a
transformation
Grades 3 – 5 ·
Identify and
describe the results of translations, reflections, and rotations Grades 6 – 8 ·
Identify,
describe, and plot transformations on a coordinate plane Grade 7 ·
Identify and
describe transformations that result in rotational and reflectional symmetry Standard 3.0 Knowledge of
Measurement B1 Measure in customary and metric units Grades 3 – 6 ·
Measure length
in customary and metric unit B2 Measure angles in polygons
Grades 5 & 6 ·
Measure angles
in a polygon Standard 7.0 Processes of
Mathematics B1 Justify ideas or solutions with mathematical
concepts or proofs 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.3 The student will use transformations
to move figures, create designs, and/or demonstrate geometric properties. Assessment Limits
Ø
Transformations
include reflections, rotations, translations, and dilations. Ø
Items should go
beyond the identification of transformations. Ø
Essential
properties and relationships include the following: congruence, similarity,
and symmetry. Ø
The student’s
explanation of a transformation must include the following: ·
translation –
distance and direction ·
reflection –
line of reflection ·
rotation –
center of rotation, angle measure, direction (clockwise or counterclockwise) ·
dilation –
center and scale factor. Ø
Paper folding
and the use of Mirasä and mirrors are appropriate methods for performing transformations,
and their use must be referenced. Skill Statement
Given one or more
transformations, the student sketches the result of the transformation(s)
and/or explains the geometric effect of the transformation(s) on the figure. 


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Standard 2.0 Knowledge of
Geometry A1 Analyze properties of plane geometric
figures Grades 3 & 5 ·
Identify
polygons within a composite figure Grades 5 & 6 ·
Identify and
describe relationships of lines and line segments Grades 3 – 6 ·
Identify,
describe, and label points, lines, rays, vertices, angles, and planes using
correct symbolic notation Grade 7 ·
Identify and
describe the angles formed by intersecting lines, line segments, and rays
including vertical, adjacent, complementary, and supplementary angles Grades 7 & 8 ·
Identify and
describe the relationships between angles formed when parallel lines are cut
by a transversal including alternate interior, alternate exterior, and
corresponding angles Grades 7 & 8 ·
Identify and
describe the relationship among the parts of a right triangle A2 Analyze geometric relationships Grade 4 ·
Compare and
classify angles in geometric figures and pictures Grade 5 ·
Compare and classify
quadrilaterals by length of sides and measures of angles Grade 6 ·
Compare and
classify triangles by sides and angle measures ·
Identify and
compare the relationship between parts of a circle Grades 6 & 7 ·
Determine a
missing angle measure using the sum of the interior angles of a polygons Grade 7 ·
Determine the
measure of angles formed by intersecting lines, line segments, and rays Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.4 The student will construct and/or draw and/or validate
properties of geometric figures using appropriate tools and technology. Assessment Limits Ø
“Validate properties”
in this indicator, means justifying solutions using definitions, mathematical
principles and/or measurement. Ø
Students may use
a compass, straightedge, patty paper, a Mira™, and/or a mirror as construction
tools. Using a ruler or protractor cannot be part of the strategy. Ø
Students may use
a compass, ruler, patty paper, a Mira™, a mirror and/or a protractor as drawing
tools. Ø
It is acceptable
to do a construction when the item asks for a drawing. Ø
Paper folding
and the use of Miras™ and mirrors are appropriate methods for representing,
constructing, and/or analyzing figures, and their use must be referenced. Ø
Constructions
and drawings are limited to the twodimensional relationships listed in
2.1.1. Skill Statement The student draws and/or
constructs geometric figures and/or justifies the solution. 
Perspective Drawings ·
The student will
use the properties of perspective drawings to draw twodimensional or
threedimensional shapes using vanishing points, lines of sight, and hidden
lines. 
Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

B1 Analyze the properties of solid geometric
figures Grades 3 – 5 ·
Identify and
describe solid geometric figures using the number of edges, faces, vertices,
or shape of base B2 Analyze the relationship between plane
geometric figures and surfaces of solid geometric figures Grades 3 – 5 ·
Compare plane
figures to surfaces of solid geometric figures C1 Represent plane geometric figures Grades
3 – 8 ·
Sketch or draw plane geometric figures Grades
7 & 8 ·
Construct geometric figures using a variety of construction tools D1 Analyze and apply the properties of
congruent and/or similar polygons Grades 3 – 7 ·
Analyze and
apply the properties of congruent polygons Grades 5 – 8 ·
Analyze and
apply the properties of similar polygons Standard 3.0 Knowledge of
Measurement B1 Measure in customary and metric units Grades 3 – 6 ·
Measure length
in customary and metric units B2 Measure
angles in polygons Grades 5 & 6 ·
Measure angles
in a polygon Standard 7.0 Processes of
Mathematics B1 Justify ideas or solutions with mathematical
concepts or proofs 
2.1 The student will represent and analyze two and threedimensional
figures using tools and technology when appropriate. 2.1.4 The student will construct and/or draw and/or validate
properties of geometric figures using appropriate tools and technology. Assessment Limits Ø
“Validate
properties” in this indicator, means justifying solutions using definitions,
mathematical principles and/or measurement. Ø
Students may use
a compass, straightedge, patty paper, a Mira™, and/or a mirror as construction
tools. Using a ruler or protractor cannot be part of the strategy. Ø
Students may use
a compass, ruler, patty paper, a Mira™, a mirror and/or a protractor as drawing
tools. Ø
It is acceptable
to do a construction when the item asks for a drawing. Ø
Paper folding
and the use of Miras™ and mirrors are appropriate methods for representing,
constructing, and/or analyzing figures, and their use must be referenced. Ø
Constructions
and drawings are limited to the twodimensional relationships listed in
2.1.1. Skill Statement The student draws and/or
constructs geometric figures and/or justifies the solution. 


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG 
Geometry
Voluntary State Curriculum (VSC) 

CLG 2 The student will demonstrate the ability to solve mathematical and realworld problems using measurement and geometric models and will justify solutions and explain processes used. 
Additional Topics for a Complete Course Would Include 

Standard 1.0 Knowledge of
Algebra, Patterns and Functions. B2 Identify, write, solve, and apply equations
and inequalities Grades
3 – 8 and Algebra/Data Analysis CLG 1.2.1 ·
Solve linear equations from onestep to variables on both sides Standard 2.0 Knowledge of
Geometry A1 Analyze properties of plane geometric
figures
Grades
3 & 5 ·Identify polygons within a
composite figure Grades
5 & 6 ·Identify and describe
relationships of lines and line segments Grades
3 – 6 ·Identify, describe, and
label points, lines, rays, vertices, angles, and planes using correct
symbolic notation Grades
7 ·Identify and describe the
angles formed by intersecting lines, line segments, and rays including
vertical, adjacent, complementary, and supplementary angles Grades
7 & 8 ·Identify and describe the
relationships between angles formed when parallel lines are cut by a
transversal including alternate interior, alternate exterior, and
corresponding angles Grades
7 & 8 ·Identify and describe the
relationship among the parts of a right triangle A2 Analyze geometric relationships
Grade
4 ·Compare and classify angles
in geometric figures and pictures Grade
5 ·Compare and classify
quadrilaterals by length of sides and measures of angles Grade
6 ·
Compare and classify triangles by sides and angle measures ·
Identify and compare the relationship between parts of a circle Grades
6 & 7 ·
Determine a missing angle measure using the sum of the interior
angles of polygons Grade
7 ·
Determine the measure of angles formed by intersecting lines, line
segments, and rays 
2.2 The student will apply geometric properties and relationships to
solve problems using tools and technology when appropriate. 2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts. Assessment Limits
Ø Students will demonstrate
geometric reasoning and justify conclusions.
Although the focus is on geometric theory, answers to some items may
include a numeric answer. Ø Corresponding measurements
include length, angle measure, perimeter, circumference, area, volume,
surface area and lateral area. Skill Statement
Ø The student recognizes
shapes as congruent or similar, calculates corresponding measurements, and/or
justifies conclusions. Ø The student uses congruency
and similarity statements to identify corresponding parts of figures. 

Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG 
Geometry
Voluntary State Curriculum (VSC) 

CLG 2 The student will demonstrate the ability to solve mathematical and realworld problems using measurement and geometric models and will justify solutions and explain processes used. 
Additional Topics for a Complete Course Would Include 

Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a transversal D1 Analyze
and apply the properties of congruent and/or
similar polygons Grades
3 – 7 ·Analyze and apply the
properties of congruent polygons Grades
5 – 8 ·Analyze and apply the
properties of similar polygons Standard 3.0 Knowledge of
measurement C1 Estimate and apply measurement formulas
Grades
3 – 7 ·Estimate and determine area
and perimeter of geometric figures Grade
6 ·
Determine the missing dimension of
rectangles Grades
6 – 8 ·Estimate and determine the
surface area and volume of geometric solids including prisms, cylinders,
cones, pyramids, and spheres Grade
8 ·
Estimate and determine the area and circumference of a circle C2 Analyze measurement relationships
Grade
7 ·
Determine the missing dimension for a figure using a scale Grade
8 ·
Use proportional reasoning to solve measurement problems 
2.2 The student will apply geometric properties and relationships to
solve problems using tools and technology when appropriate. 2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts. Assessment Limits
Ø Students will demonstrate
geometric reasoning and justify conclusions.
Although the focus is on geometric theory, answers to some items may
include a numeric answer. Ø Corresponding measurements
include length, angle measure, perimeter, circumference, area, volume,
surface area and lateral area. Skill Statement
Ø The student recognizes
shapes as congruent or similar, calculates corresponding measurements, and/or
justifies conclusions. Ø The student uses congruency
and similarity statements to identify corresponding parts of figures. 

Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data Analysis CLG 
Geometry
Voluntary State Curriculum (VSC) 

CLG 2 The student will demonstrate the ability to solve mathematical and realworld problems using measurement and geometric models and will justify solutions and explain processes used. 
Additional Topics for a Complete Course Would Include 

Standard 6.0 Knowledge of
Number Relationships or Computation C3 Analyze ratios, proportions, or percents
Grades
6 – 8 ·Determine or use ratios,
unit rates, and percents, in the context of the problem Grade
8 ·
Solve problems using proportional reasoning Standard 7.0 Processes of
Mathematics B1 Justify ideas
or solutions with mathematical concepts or proofs 
2.2 The student will apply geometric properties and relationships to
solve problems using tools and technology when appropriate. 2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts. Assessment Limits
Ø Students will demonstrate
geometric reasoning and justify conclusions.
Although the focus is on geometric theory, answers to some items may
include a numeric answer. Ø Corresponding measurements
include length, angle measure, perimeter, circumference, area, volume,
surface area and lateral area. Skill Statement
Ø The student recognizes
shapes as congruent or similar, calculates corresponding measurements, and/or
justifies conclusions. Ø The student uses congruency
and similarity statements to identify corresponding parts of figures. 


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Standard 1.0 Knowledge of Algebra, Patterns and Functions B2 Identify,
write, solve, and apply equations and inequalities
Grades
3 – 8 and Algebra/Data Analysis CLG 1.2.1 ·
Solve linear equations from onestep to variables on both sides Standard 2.0 Knowledge of Geometry
A2 Analyze geometric relationships
Grade
4 ·
Compare and classify angles in geometric figures and pictures Grade
5 ·
Compare and classify quadrilaterals by length of sides and measures
of angles Grade
6 ·
Compare and classify triangles by sides and angle measures ·
Identify and compare the relationship between parts of a circle Grades
6 & 7 ·
Determine a missing angle measure using the sum of the interior
angles of a polygon Grade
7 ·
Determine the measure of angles formed by intersecting lines, line
segments, and rays Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal ·
Use the Pythagorean Theorem to solve problems Standard 6.0 Knowledge of Number Relationships or Computation C1 Analyze number relationships and compute
Grades
7 & 8 ·
Calculate powers of integers and square roots of perfect square whole
numbers 
2.2 The student will apply geometric properties and relationships to
solve problems using tools and technology. 2.2.2 The student will solve problems using twodimensional figures
and/or righttriangle trigonometry. Assessment Limits
Ø Students will demonstrate
geometric reasoning and justify conclusions. Ø Trigonometric functions may
be used to find sides or angles. Ø Trigonometric functions
will be limited to sine, cosine, and tangent and their inverses. Skill Statement
The
student solves a problem involving missing parts of twodimensional figures,
which may require the use of righttriangle trigonometry, the Pythagorean
theorem, or special right triangle relationships. 
Trigonometry
·
The student will apply the Law of Sines and the Law of Cosines to
solve problems involving oblique triangles. ·
The student will solve problems using the secant, cosecant, and
cotangent functions. Similarity/Right
Triangles
·
The student will use geometric mean and relationships between parts of
a right triangle and the altitude drawn to the hypotenuse to find missing
parts of right triangles. 
Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Standard 2.0
Knowledge of Geometry
A1 Analyze properties of plane geometric
figures
Grades
5 & 6 ·
Identify and describe relationships of lines and line segments Grade
7 ·
Identify and describe the angles formed by intersecting lines, line
segments, and rays including vertical, adjacent, complementary, and
supplementary angles Grades
7 & 8 ·
Identify and describe the relationships between angles formed when
parallel lines are cut by a transversal including alternate interior,
alternate exterior, and corresponding angles Grades
7 & 8 ·
Identify and describe the relationship among the parts of a right
triangle A2 Analyze geometric relationships
Grade
4 ·
Compare and classify angles in geometric figures and pictures Grade
5 ·
Compare and classify quadrilaterals by length of sides and measures
of angles Grade
6 ·
Compare and classify triangles by sides and angle measures ·
Identify and compare the relationship between parts of a circle Grades
6 & 7 ·
Determine a missing angle measure using the sum of the interior
angles of a polygon Grade
7 ·
Determine the measure of angles formed by intersecting lines, line
segments, and rays Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal ·
Use the Pythagorean Theorem to solve problems B1 Analyze the properties of solid geometric
figures
Grades
3 – 5 ·
Identify and describe solid geometric figures using the number of
edges, faces, vertices, or shape of base 
2.2 The student will apply geometric properties and relationships to
solve problems using tools and technology when appropriate. 2.2.3 The student will use inductive or deductive reasoning. Assessment Limits
Ø Students are expected to
demonstrate their geometric reasoning and justify conclusions. Although the focus is on geometric theory,
answers to some questions may include a numeric answer. Ø Items may include geometric
applications, patterns, and logic, including syllogisms. Ø Narrative, flow chart, or
twocolumn proof may be used as a valid argument. Skill Statement
Given
a situation, the student arrives at or justifies a conclusion using inductive
or deductive reasoning. 
Algebraic Proofs
·
The student will write algebraic proofs. 
Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

D1 Analyze and apply the properties of
congruent and/or similar polygons
Grades 3 – 7 ·
Analyze and apply the properties of congruent polygons Grades
5 – 8 ·
Analyze and apply the properties of similar polygons Standard 7.0
Processes of Mathematics
B1 Justify ideas or solutions with mathematical concepts or proofs 
2.2 The student will apply geometric properties and relationships to
solve problems using tools and technology when appropriate. 2.2.3 The student will use inductive or deductive reasoning. Assessment Limits
Ø Students are expected to
demonstrate their geometric reasoning and justify conclusions. Although the focus is on geometric theory,
answers to some questions may include a numeric answer. Ø Items may include geometric
applications, patterns, and logic, including syllogisms. Ø Narrative, flow chart, or
twocolumn proof may be used as a valid argument. Skill
Statement
Given
a situation, the student arrives at or justifies a conclusion using inductive
or deductive reasoning. 


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Standard
1.0 Knowledge of Algebra, Patterns, or Function B2 Identify, write, solve, and apply equations
and inequalities Grades
3 – 8 and Algebra/Data Analysis CLG 1.2.1 ·
Solve linear equations from onestep to variables on both sides Grades
6 – 8 and Algebra/Data Analysis CLG 1.2.2 ·
Solve linear inequalities Grades
6 – 8 and Algebra/Data Analysis CLG 1.2.5 ·
Apply given formulas in a problemsolving situation Standard
2.0 Knowledge of Geometry A2 Analyze geometric
relationships Grades 6 & 7 ·
Determine a missing angle measure using the sum of interior angles of
a polygon Grade 8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal ·
Use the Pythagorean Theorem to solve problems D1 Analyze and apply
the properties of congruent and/or similar polygons Grades 3 – 7 ·
Analyze and apply the properties of congruent polygons Grades 5 – 8 ·
Analyze and apply the properties of similar polygons Standard 3.0 Knowledge of Measurement B1 Measure in customary
and metric units Grades 3 – 6 ·
Measure length in customary and metric units 
2.3
The student will apply concepts of measurement using tools and technology
when appropriate. 2.3.1
The student will use algebraic and/or geometric properties to measure
indirectly. Assessment Limits Ø “Measure indirectly” means
to use mathematical concepts such as congruence, similarity, and ratio and
proportion to calculate measurements. Ø Similarity and congruence
will be directly stated or implied (scale drawings, enlargements.) Ø Items may require the
student to make comparisons. Ø This indicator may
incorporate measuring. Ø This indicator does not
include righttriangle trigonometry. Skill Statement The student calculates measurements indirectly by using mathematical concepts. Ø


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

B2
Measure angles in polygons Grades
5 & 6 ·
Measure angles in polygons C1
Estimate and apply measurement formulas Grades
3 – 7 ·
Estimate and determine the area and perimeter of geometric figures Grades
6 – 8 ·
Estimate and determine the surface area and volume of geometric
solids including prisms, cylinders, cones, pyramids, and spheres Grade
8 ·
Estimate and determine the area and circumference of a circle C2
Analyze measurement relationships Grade
7 ·
Determine a missing dimension for a figure using a scale Grade
8 ·
Use proportional reasoning to solve measurement problems Standard
6.0 Knowledge of Number Relationships or Computation C3
Analyze ratios, proportions, or percents Grades
6 – 8 ·
Determine or use ratios, unit rates, and percents, in the context of
the problem 
2.3
The student will apply concepts of measurement using tools and technology
when appropriate. 2.3.1
The student will use algebraic and/or geometric properties to measure
indirectly. Assessment Limits Ø
“Measure indirectly” means to use mathematical concepts such as
congruence, similarity, and ratio and proportion to calculate measurements. Ø
Similarity and congruence will be directly stated or implied (scale
drawings, enlargements.) Ø
Items may require the student to make comparisons. Ø
This indicator may incorporate measuring. Ø
This indicator does not include righttriangle trigonometry. Skill Statement The student calculates measurements indirectly by using mathematical concepts. Ø


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain processes
used. 
Additional Topics for a Complete Course
Would Include 

Standard 1.0 Knowledge of
Algebra, Patterns, or Functions B2 Identify, write, solve, and apply equations
and inequalities
Grades
3 – 8 and Algebra/Data Analysis CLG 1.2.1 ·
Solve linear equations from onestep to variables on both sides Grades
6 – 8 and Algebra/Data Analysis CLG 1.2.2 ·
Solve linear inequalities Grades
6 – 8 and CLG 1.2.5 ·
Apply given formulas in a problemsolving situation Standard 2.0 Knowledge of
Geometry A1 Analyze properties of plane geometric
figures
Grades
3 & 5 ·
Identify polygons within a composite figure Grades 5 & 6 ·
Identify and describe relationships of lines and line segments Grades
3 – 6 ·
Identify, describe, and label points, lines, rays, vertices, angles,
and planes using correct symbolic notation Grade
7 ·
Identify and describe the angles formed by intersecting lines, line
segments, and rays including vertical, adjacent, complementary, and
supplementary angles Grades
7 & 8 ·
Identify and describe the relationships between angles formed when
parallel lines are cut by a transversal including alternate interior,
alternate exterior, and corresponding angles Grades
7 & 8 ·
Identify and describe the relationship among the parts of a right
triangle A2 Analyze geometric relationships
Grade
4 ·
Compare and classify angles in geometric figures and pictures Grade
5 ·
Compare and classify quadrilaterals by length of sides and measures
of angles

2.3 The student will apply concepts of measurement using tools and
technology when appropriate. 2.3.2 The student will use techniques of measurement and will
estimate, calculate, and/or compare perimeter, circumference, area, volume,
and/or surface area of two and threedimensional figures and their
parts. Assessment Limits
Ø Twodimensional shapes
include polygons, circles, and composite figures. Ø Threedimensional shapes
include cubes, prisms, pyramids, cylinders, cones, spheres, and composite
figures. Ø Formulas will be
provided. Ø No oblique solids will be
used. Ø Items may involve
applications of geometric properties and relationships. Ø Students may be required to
make comparisons which do not require calculations. Skill Statement
The
student solves a problem involving perimeter, area, surface area, lateral
area, circumference, and/or volume expressing solutions with appropriate
units. 
Circles
·
The student will determine the area of a sector. ·
The student will determine the length of an arc. Solid Geometric Figures
·
The student will determine properties of oblique solid geometric
figures. * ·
The student will determine properties of pyramids that have
nonsquare bases. 
Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Grade 6 ·
Compare and classify triangles by sides and angle measures ·
Identify and compare the relationship between parts of a circle Grades
6 & 7 ·
Determine a missing angle measure using the sum of the interior
angles of a polygon Grade
7 ·
Determine the measure of angles formed by intersecting lines, line
segments, and rays Grade
8 ·
Determine the measure of angles formed by parallel lines cut by a
transversal B1 Analyze the properties of solid geometric
figures
Grades
3 – 5 ·
Identify and describe solid geometric figures using the number of
edges, faces, vertices, or shape of base B2 Analyze the relationship between plane
geometric figures and surfaces of solid geometric figures
Grades
3 – 5 ·
Compare a plane figure to surfaces of solid geometric figures C1 Represent plane geometric
figures
Grades
3 – 8 ·
Sketch or draw plane geometric figures using a variety of tools Standard
3.0 Knowledge of Measurement C1 Estimate and apply measurement formulas Grades
3 – 7 ·
Estimate and determine the area and perimeter of geometric figures Grades
6 – 8 ·
Estimate and determine the surface area and volume of geometric
solids including prisms, cylinders, cones, pyramids, and spheres Grade
8

2.3 The student will apply concepts of measurement using tools and
technology when appropriate. 2.3.2 The student will use techniques of measurement and will
estimate, calculate, and/or compare perimeter, circumference, area, volume,
and/or surface area of two and threedimensional figures and their
parts. Assessment Limits
Ø Twodimensional shapes
include polygons, circles, and composite figures. Ø Threedimensional shapes
include cubes, prisms, pyramids, cylinders, cones, spheres, and composite
figures. Ø Formulas will be
provided. Ø No oblique solids will be
used. Ø Items may involve
applications of geometric properties and relationships. Ø Students may be required to
make comparisons which do not require calculations. Skill Statement
The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units. 


Voluntary
State Curriculum – Geometry
Prerequisites Summarized from Voluntary
State Curriculum Mathematics Grades 3 – 8 and Algebra/Data
Analysis CLG 
Geometry Voluntary State Curriculum (VSC) 

CLG 2 The student will
demonstrate the ability to solve mathematical and realworld problems using
measurement and geometric models and will justify solutions and explain
processes used. 
Additional Topics for a Complete Course
Would Include 

Standard 6.0 Knowledge of
Number Relationships or Computation C2 Apply estimation strategies Grades
3 – 8 Use estimation to determine the reasonableness of an answer 
2.3 The student will apply concepts of measurement using tools and
technology when appropriate. 2.3.2 The student will use techniques of measurement and will
estimate, calculate, and/or compare perimeter, circumference, area, volume,
and/or surface area of two and threedimensional figures and their
parts. Assessment Limits
Ø Twodimensional shapes
include polygons, circles, and composite figures. Ø Threedimensional shapes
include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.
Ø Formulas will be
provided. Ø No oblique solids will be
used. Ø Items may involve
applications of geometric properties and relationships. Ø Students may be required to
make comparisons which do not require calculations. Skill Statement
The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units. 
