Download Geometry Curriculum Guide

BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
First 9 Weeks
Prerequisite Knowledge
Constructions (G.4)
Reasoning, Lines and Transformations
(G.1)
Parallel and Perpendicular Lines (G.2,
G.3b)
Second 9 Weeks
Congruent Triangles (G.6)
Triangle Inequality (G.5)
Similar Triangles (G.7)
Third 9 Weeks
Fourth 9 Weeks
Right Triangles (G.8)
Circles (G.11, G.12)
Quadrilaterals & Polygons (G.9, G.10) Surface Area & Volume (G.13)
Symmetry & Transformations (G.3c, d) Similar Solids (G.14)
1st Nine Weeks
Dates
Block
3 days
Trdtl
6 days
Standards/Essential Questions
Essential Knowledge/Skills/Understanding
Standard: Prerequisite for G.3, G.4
The student will use pictorial
representations, including
computer software,
constructions, and coordinate
methods, to solve problems
involving symmetry and
transformation. This will include
a) investigating and using
formulas for finding distance,
midpoint,
Notes:
 A point is a location in space. It has no
length, width, or height. A point is
usually named with a capital letter.
 A line is a collection of points going on
and on infinitely in both directions. It
has no endpoints. When a line is
drawn, at least two points on it can be
marked and given capital letter names.
Arrows must be drawn to show that
the line goes on in both directions
infinitely (e.g., AB , read as “the line
AB”).
 A line segment is part of a line. It has
two endpoints and includes all the
points between those endpoints. To
name a line segment, name the
endpoints (e.g., AB , read as “the line
segment AB”).
Resources
Key Vocabulary
acute
angle
bisect
collinear
complementary
coplanar
horizontal
intersect
line
obtuse
plane
point
postulate
ray
right [angle]
segment
supplementary
theorem
vertex
vertical
DOE Lesson Plans
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Textbook Resources
1.1 – 1.3
Resources/Lessons
BCPS Resources
NCTM
Dates
Standards/Essential Questions
Block
Trdtl
Standard: Prereq. for G.2, G.10
2 days
4 days
The student will use the
relationships between angles
formed by two lines cut by a
transversal
SOL 8.6a: Verify/describe
relationships among
vertical/adjacent/supplementary/
complementary angles
Essential Knowledge/Skills/Understanding
Notes:
 A ray is part of a line. It has one
endpoint and continues infinitely in
one direction. To name a ray, say the
name of its endpoint first and then say
the name of one other point on the
ray (e.g., AB , read as “the ray AB”).
 Two rays that have the same endpoint
form an angle. This endpoint is called
the vertex. Angles are found wherever
lines and line segments intersect. An
angle can be named in three different
ways by using
- three letters to name, in this order, a
point on one ray, the vertex, and a
point on the other ray;
- one letter at the vertex; or
- a number written inside the rays of
the angle.
 Intersecting lines have one point in
common.
Resources
Key Vocabulary
adjacent angles
alternate exterior angles
alternate interior angles
complementary angles
consecutive (sameside) interior angles
corresponding angles
exterior angle
interior angle
intersection
linear pair
parallel
perpendicular
skew
supplementary angles
theorem
transversal
DOE Lesson Plans
Textbook Resources
1.4, 1.5
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Resources/Lessons
Dates
Block
Trdtl
1 day
2 days
Standards/Essential Questions
Essential Knowledge/Skills/Understanding
Standard:G.4
The student will construct and
justify the constructions of
a) a line segment congruent to a
given line segment;
b) the perpendicular bisector of a
line segment;
e) the bisector of a given angle;
f) an angle congruent to a given
angle
Prerequisite/Extension SOL
6.12 determine congruence of
segments/angles/polygons
Essential Understandings
 Construction techniques are used to solve realworld problems in engineering, architectural
design, and building construction.
 Construction techniques include using a
straightedge and compass, paper folding, and
dynamic geometry software.
Essential Knowledge/Skills
 Construct and justify the constructions of
– a line segment congruent to a given line
segment;
– the perpendicular bisector of a line
segment;
– the bisector of a given angle;
– an angle congruent to a given angle; and
Resources
Key Vocabulary
bisector
centroid
circumcenter
circumscribed
compass
congruence
construction
incenter
inscribed
intersection
parallel lines
perpendicular bisector
perpendicular lines
bisector
straightedge
transversal
DOE Lesson Plans
Constructions
Textbook Resources
1.6
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Block
Trdtl
Standards/Essential Questions
Standard: G.3
1 day
The student will use pictorial
representations, including
computer software,
constructions, and coordinate
methods, to solve problems
involving symmetry and
transformation. This will include
a) investigating and using
formulas for finding distance,
midpoint,
Essential Knowledge/Skills/Understanding
Essential Understanding
2 days

A.6 graph linear equations/linear
inequal (2 vars) ‐ a) determine slope
of line given equation of line/graph of
line or two points on line ‐ slope as
rate of change; b) write equation of
line given graph of line/two points on
line or slope‐point on line
8.8 a) apply transformations to plane
figures; b) ID applications of
transformations
7.8 represent transformations
(reflections, dilations, rotations, and
translations) of polygons in the
coordinate plane by graphing
Key Vocabulary
slope
midpoint formula
distance formula
slope formula
Essential Knowledge/Skills


Prerequisite/Extension SOL
The distance formula is an application of
the Pythagorean Theorem.
Resources
Find the coordinates of the midpoint
of a segment, using the midpoint
formula.
Apply the distance formula to find
the length of a line segment when
given the coordinates of the
endpoints.
DOE Lesson Plans
Distance & Midpoint Formulas
Textbook Resources
1.7
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Block
Trdtl
Standards/Essential Questions
Standard: G.1
Essential Knowledge/Skills/Understanding
Essential Understanding
7 days
14 days The student will construct and judge the
validity of a logical argument consisting
of a set of premises and a conclusion.
This will include
a) identifying the converse, inverse,
and contrapositive of a conditional
statement;
b) translating a short verbal argument
into symbolic form;
c) using Venn diagrams to represent
set relationships; and
d) using deductive reasoning.

Inductive reasoning, deductive reasoning, and
proof are critical in establishing general claims.

Deductive reasoning is the method that uses logic
to draw conclusions based on definitions,
postulates, and theorems.

Inductive reasoning is the method of drawing
conclusions from a limited set of observations.

Proof is a justification that is logically valid and
based on initial assumptions, definitions,
postulates, and theorems.

Logical arguments consist of a set of premises or
hypotheses and a conclusion.

Euclidean geometry is an axiomatic system based
on undefined terms (point, line and plane),
postulates, and theorems.

When a conditional and its converse are true, the
statements can be written as a biconditional, i.e.,
iff or if and only if.

Logical arguments that are valid may not be true.
Truth and validity are not synonymous.
Resources
Key Vocabulary
algebraic method
assumption
biconditional statement
conclusion
conditional statement
conjecture
contrapositive
converse
coordinate method
counterexample
deductive reasoning
hypothesis (premise)
inductive reasoning
inverse
Law of Detachment
Law of Syllogism
Law of the
Contrapositive
oblique
postulate (axiom)
proof
symbolic form
union
Venn diagram
vertical angles
DOE Lesson Plans
Logic & Conditional Statements
Inductive & Deductive Reasoning
Textbook Resources
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Chapter 2
Essential Knowledge/Skills
 Identify the converse, inverse, and contrapositive
of a conditional statement.
 Translate verbal arguments into symbolic form,
such as (p  q) and (~p  ~q).
 Determine the validity of a logical argument.
 Use valid forms of deductive reasoning, including
the law of syllogism, the law of the contrapositive,
the law of detachment, and counterexamples.
 Select and use various types of reasoning and
methods of proof, as appropriate.
 Use Venn diagrams to represent set relationships,
such as intersection and union.
 Interpret Venn diagrams.
 Recognize and use the symbols of formal logic,
which include →, ↔, ~,  ,  , and  .
Resources/Lessons
Supplemental Lessons for Venn
diagrams
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Block
Trdtl
Standards/Essential Questions
Standard: G.2
Essential Knowledge/Skills/Understanding
Essential Understanding
2 day
4 days
The student will use the relationships
between angles formed by two lines cut 
by a transversal to
a) determine whether two lines are

parallel;
b) verify the parallelism, using
algebraic and coordinate methods
as well as deductive proofs; and

c) solve real-world problems
involving angles formed when
parallel lines are cut by a
transversal.
Parallel lines intersected by a transversal form
angles with specific relationships.
Some angle relationships may be used when
proving two lines intersected by a transversal are
parallel.
The Parallel Postulate differentiates Euclidean
from non-Euclidean geometries such as spherical
geometry and hyperbolic geometry.
Resources
Key Vocabulary
alternate exterior angles
alternate interior angles
consecutive (sameside) interior angles
corresponding angles
exterior angle
interior angle
parallel
perpendicular
skew
transversal
DOE Lesson Plans
Lines & Angles
Essential Knowledge/Skills
Prerequisite/Extension SOL
A.6 graph linear equations/linear inequal (2
vars) ‐ a) determine slope of line given
equation of line/graph of line or two points
on line ‐ slope as rate of change; b) write
equation of line given graph of line/two
points on line or slope‐point on line
8.6 a) verify/describe relationships among
vertical/adjacent/
supplementary/complementary angles;
 Use algebraic and coordinate methods as well as
deductive proofs to verify whether two lines are
parallel.
 Solve problems by using the relationships between
pairs of angles formed by the intersection of two
parallel lines and a transversal including
corresponding angles, alternate interior angles,
alternate exterior angles, and same-side
(consecutive) interior angles.
 Solve real-world problems involving intersecting
and parallel lines in a plane.
Textbook Resources
3.1 – 3.4
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Block
Trdtl
1day
2 days
Standards/Essential Questions
Standard:G.4
The student will construct and justify
the constructions of
c) a perpendicular to a given line
from a point not on the line;
d) a perpendicular to a given line at a
given point on the line;
g) a line parallel to a given line
through a point not on the given
line.
Essential Knowledge/Skills/Understanding
Essential Understandings
 Construction techniques are used to solve realworld problems in engineering, architectural design,
and building construction.
 Construction techniques include using a
straightedge and compass, paper folding, and
dynamic geometry software.
Essential Knowledge/Skills
 Construct and justify the constructions of
–
–
–
a perpendicular to a given line from a point
not on the line;
a perpendicular to a given line at a point on
the line;
a line parallel to a given line through a point
not on the given line.
Resources
Key Vocabulary
bisector
centroid
circumcenter
circumscribed
compass
congruence
construction
incenter
inscribed
intersection
parallel lines
perpendicular bisector
perpendicular lines
bisector
straightedge
transversal
DOE Lesson Plans
Constructions
Textbook Resources
3.6
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Block
Trdtl
Standards/Essential Questions
Standard: G.3
2 day
The student will use pictorial
representations, including computer
software, constructions, and coordinate
methods, to solve problems involving
symmetry and transformation. This will
include
b) applying slope to verify and determine
whether lines are parallel or
perpendicular;
Essential Knowledge/Skills/Understanding
Resources
Key Vocabulary
Essential Understanding
4 days
 Parallel lines have the same slope.
 The product of the slopes of perpendicular lines is -1.
Textbook Resources
3.7, 3.8
Resources/Lessons
Essential Knowledge/Skills
 Use a formula to find the slope of a line.
 Compare the slopes to determine whether two lines
are parallel, perpendicular, or neither.
Performance Task must be completed and graded on rubric by the end of Quarter 1
Sample Performance Tasks: (Exemplars)
 Parallel or Not, That’s The Question
 Differences of Reversed Squares
DOE Lesson Plans
Slope
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
2nd Nine Weeks
Dates
Standards/Essential Questions
Block
Trdtl
Standard: G.10
½ days
1 day
The student will solve real-world
problems involving angles of polygons.
Dates
Standards/Essential Questions
Block
Trdtl
Standard: G.6
6 days
12 days
The student, given information in the
form of a figure or statement, will prove
two triangles are congruent, using
algebraic and coordinate methods as
well as deductive proofs.
Essential Knowledge/Skills/Understanding
Resources
Key Vocabulary
Essential Knowledge/Skills
DOE Lesson Plans
 Solve real-world problems involving the measures
of interior and exterior angles of polygons.
Textbook Resources
3.5
Note: This section involves only interior and exterior angles
in triangles.
Resources/Lessons
Essential Knowledge/Skills/Understanding
Essential Understanding
 Congruence has real-world applications in a variety
of areas, including art, architecture, and the
sciences.
 Congruence does not depend on the position of the
triangle.
 Concepts of logic can demonstrate congruence or
similarity.
 Congruent figures are also similar, but similar
figures are not necessarily congruent.
Essential Knowledge/Skills
 Use definitions, postulates, and theorems to prove
triangles congruent.
 Use coordinate methods, such as the distance
formula and the slope formula, to prove two
triangles are congruent.
 Use algebraic methods to prove two triangles are
congruent.
Resources
Key Vocabulary
SSS (side-side-side)
SAS (side-angle-side)
ASA (angle-side-side)
AAS (angle-angle-side)
Scalene
Isosceles – legs, vertex angle
Equilateral
Acute
Obtuse
Equiangular
Right
DOE Lesson Plans
Congruent Triangles
Textbook Resources
Chapter 4
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Standards/Essential Questions
Block
Trdtl
Standard: G.5
3 days
6 days
The student, given information
concerning the lengths of sides and/or
measures of angles in triangles, will
a) order the sides by length, given the
angle measures;
b) order the angles by degree
measure, given the side lengths;
c) determine whether a triangle
exists; and
d) determine the range in which the
length of the third side must lie.
These concepts will be considered in the
context of real-world situations.
Essential Knowledge/Skills/Understanding
Essential Understanding
 The longest side of a triangle is opposite the largest
angle of the triangle and the shortest side is
opposite the smallest angle.
 In a triangle, the length of two sides and the
included angle determine the length of the side
opposite the angle.
 In order for a triangle to exist, the length of each
side must be within a range that is determined by
the lengths of the other two sides.
Essential Knowledge/Skills
 Order the sides of a triangle by their lengths when
given the measures of the angles.
 Order the angles of a triangle by their measures
when given the lengths of the sides.
 Given the lengths of three segments, determine
whether a triangle could be formed.
 Given the lengths of two sides of a triangle,
determine the range in which the length of the third
side must lie.
 Solve real-world problems given information about
the lengths of sides and/or measures of angles in
Resources
Key Vocabulary
altitude
isosceles
linear pair
median
scalene
triangle
Triangle Inequality Theorem
DOE Lesson Plans
How Many Triangles?
Textbook Resources
5.1 – 5.4 (supplemental to G.5), 5.6,
5.7
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
triangles.
Dates
Block
Trdtl
5 days
10 days
Standards/Essential Questions
Standard: G.7
The student, given information in the
form of a figure or statement, will
prove two triangles are similar, using
algebraic and coordinate methods as
well as deductive proofs.
Essential Knowledge/Skills/Understanding
Essential Understanding
 Similarity has real-world applications in a variety of
areas, including art, architecture, and the sciences.
 Similarity does not depend on the position of the
triangle.
 Congruent figures are also similar, but similar
figures are not necessarily congruent.
Prerequisite/Extension SOL
6.12 determine congruence of
segments/angles/polygons
7.6 determine similarity of plane
figures and write proportions to
express relationships between similar
quads and triangles
Essential Knowledge/Skills
 Use definitions, postulates, and theorems to prove
triangles similar.
Resources
Key Vocabulary
area
deductive proof
perimeter
proportion
ratio
scale factor
similar figures
similar triangles
AA Similarity
SSS Similarity
SAS Similarity
volume

Use algebraic methods to prove that triangles are
similar.
DOE Lesson Plans
Similar Triangles

Use coordinate methods, such as the distance
formula, to prove two triangles are similar.
Textbook Resources
5.1 – 5.4 (supplemental to G.5), 5.6,
5.7
Resources/Lessons
Section 7.1-7.5
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Performance Task must be completed and graded on rubric by the end of Quarter 2
Sample Performance Tasks:
3rd Quarter
Dates
Block
Trdtl
7.5days
15 days
Standards/Essential Questions
Standard: G.8
The student will solve real-world
problems involving right triangles by
using the Pythagorean Theorem and its
converse, properties of special right
triangles, and right triangle
trigonometry.
Prerequisite/Extension SOL
8.10 a) verify the Pythagorean
Theorem; b) apply the Pythagorean
Theorem
A.3 express sq roots/cube roots of
whole numbers/the square root of
monomial alg exp (simplest radical
form)
A.4 solve multistep linear/ quad
equation (2 vars) ‐ a) solve literal
equation; b) justify steps used in
Essential Knowledge/Skills/Understanding
Resources
Essential Understanding
 The Pythagorean Theorem is essential for solving
problems involving right triangles.
Key Vocabulary
angle of depression
angle of elevation
area of a triangle
cosine
hypotenuse
Pythagorean Theorem
right triangle
sine
tangent
trigonometry
45°-45°-90° triangle
30°-60°-90° triangle
 The relationships between the sides and angles of right
triangles are useful in many applied fields.
 Some practical problems can be solved by choosing an
efficient representation of the problem.
 The ratios of side lengths in similar right triangles
(adjacent/hypotenuse or opposite/hypotenuse) are
independent of the scale factor and depend only on the
angle the hypotenuse makes with the adjacent side,
thus justifying the definition and calculation of
trigonometric functions using the ratios of side lengths
for similar right triangles.
Essential Knowledge/Skills
 Determine whether a triangle formed with three given
lengths is a right triangle.
DOE Lesson Plans
Pythagorean Theorem
Special Right Triangles
Textbook Resources
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
simplifying expresessions and solving
equations; c) solve quad equations
(alg/graph); d) solve multistep linear
equations (alg/graph)
 Solve for missing lengths in geometric figures, using
properties of 45-45-90 triangles.
Chapter 8: 8.1 – 8.5
 Solve for missing lengths in geometric figures, using
properties of 30-60-90 triangles.
Resources/Lessons
 Solve problems involving right triangles, using sine,
cosine, and tangent ratios.
 Solve real-world problems, using right triangle
trigonometry and properties of right triangles.
 Explain and use the relationship between the sine and
cosine of complementary angles
Dates
Block
Trdtl
1 day
1 ½ days
Standards/Essential Questions
Standard: G.10
The student will solve real-world
problems involving angles of
polygons.
Essential Knowledge/Skills/Understanding
Essential Understanding
 Two intersecting lines form angles with specific
relationships.
 Find the measure of each interior and exterior angle of
a regular polygon.
Key Vocabulary
concave
convex
pentagon
polygon
quadrilateral
regular/irregular polygon
diagonal
dodecagon
exterior angle
heptagon
hexagon
interior angle
isosceles
n-gon
nonagon
octagon
decagon
 Find the number of sides of a regular polygon, given
DOE Lesson Plans
 An exterior angle is formed by extending a side of a
polygon.
 The exterior angle and the corresponding interior angle
form a linear pair.
Prerequisite/Extension SOL
A.4 solve multistep linear/ quad
equation (2 vars) ‐ a) solve literal
equation; b) justify steps used in
simplifying expresessions and solving
equations; c) solve quad equations
(alg/graph); d) solve multistep linear
equations (alg/graph)
6.12 determine congruence of
segments/angles/polygon
Resources
 The sum of the measures of the interior angles of a
convex polygon may be found by dividing the interior
of the polygon into nonoverlapping triangles.
Essential Knowledge/Skills
 Find the sum of the measures of the interior and
exterior angles of a convex polygon.
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
the measures of interior or exterior angles of the
polygon.
 Solve real-world problems involving the measures of
interior and exterior angles of polygons.
Angles in Polygons
Textbook Resources
Chapter 6: 6.1
Resources/Lessons
Dates
Standards/Essential Questions
Block
Trdtl
8 days
12 days
Standard: G.9
Essential Knowledge/Skills/Understanding
The student will verify characteristics
of quadrilaterals and use properties of
quadrilaterals to solve real-world
problems.
Essential Understanding
 The terms characteristics and properties can be used
interchangeably to describe quadrilaterals. The term
characteristics is used in elementary and middle school
mathematics.
Prerequisite/Extension SOL
 Quadrilaterals have a hierarchical nature based on the
relationships between their sides, angles, and diagonals.
A.4 solve multistep linear/ quad
equation (2 vars) ‐ a) solve literal
equation; b) justify steps used in
simplifying expresessions and solving
equations; c) solve quad equations
(alg/graph); d) solve multistep linear
equations (alg/graph)
7.7 compare/contrast quadrilaterals
based on properties
6.13 ID/describe properties of
quadrilaterals
 Characteristics of quadrilaterals can be used to identify
the quadrilateral and to find the measures of sides and
angles.
Essential Knowledge/Skills
 Solve problems, including real-world problems, using
the properties specific to parallelograms, rectangles,
rhombi, squares, isosceles trapezoids, and trapezoids.
 Prove that quadrilaterals have specific properties, using
coordinate and algebraic methods, such as the distance
formula, slope, and midpoint formula.
 Prove the characteristics of quadrilaterals, using
deductive reasoning, algebraic, and coordinate
Resources
Key Vocabulary
base
base angles
characteristics
diagonal
isosceles trapezoid
kite
legs
median of a trapezoid
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid
DOE Lesson Plans
Properties of Quadrilaterals
Textbook Resources
Chapter 6: 6.2 – 6.7
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
methods.
Resources/Lessons
 Prove properties of angles for a quadrilateral inscribed
in a circle.†
Dates
Block
Trdtl
3 days
5 days
Standards/Essential Questions
Standard: G.3
The student will use pictorial
representations, including computer
software, constructions, and
coordinate methods, to solve
problems involving symmetry and
transformation. This will include
c) investigating symmetry and
determining whether a figure is
symmetric with respect to a line or a
point; and
d) determining whether a figure has
been translated, reflected, rotated,
or dilated, using coordinate
methods.
Prerequisite/Extension SOL
8.8 a) apply transformations to plane
figures; b) ID applications of
transformations
7.8 represent transformations
Essential Knowledge/Skills/Understanding
Essential Understanding
 Transformations and combinations of transformations
can be used to describe movement of objects in a plane.
 The image of an object or function graph after an
isomorphic transformation is congruent to the preimage
of the object.
Essential Knowledge/Skills
 Determine whether a figure has point symmetry, line
symmetry, both, or neither.
 Given an image and preimage, identify the
transformation that has taken place as a reflection,
rotation, dilation, or translation.
Resources
Key Vocabulary
Dilation
Line symmetry
Symmetry
Transformation
Translation
Rotation
Reflection
Preimage
DOE Lesson Plans
Symmetry
Transformations
Textbook Resources
Chapter 9
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
(reflections, dilations, rotations, and
translations) of polygons in the
coordinate plane by graphing
Performance Task must be completed and graded on rubric by the end of Quarter 3
Sample Performance Tasks: (Exemplars)
 Buried treasure
4th Nine Weeks
Dates
Standards/Essential Questions
Essential Knowledge/Skills/Understanding
Block
Trdtl
Standard: G.11
Essential Understanding
10 days
15 days
The student will use angles, arcs,
chords, tangents, and secants to
a) investigate, verify, and apply
properties of circles;
b) solve real-world problems
involving properties of circles;
and
c) find arc lengths and areas of
sectors in circles.
 Many relationships exist between and among angles,
arcs, secants, chords, and tangents of a circle.
Prerequisite/Extension SOL
6.10 a) define π; b) solve practical problems
w/circumference/area of circle; c) solve
 All circles are similar.
 A chord is part of a secant.
 Real-world applications may be drawn from
architecture, art, and construction.
Essential Knowledge/Skills
 Find lengths, angle measures, and arc measures
Resources
Key Vocabulary
Radius
Diameter
Chord
Arc
Secant
Tangent
Central Angle
Inscribed Angle
Sector
DOE Lesson Plans
Angles, Arcs, & Segments in
Circles
Arc Length & Area of a Sector
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
practical problems involving area and
perimeter given radius/diameter; d)
describe/determine volume/surface area of
rectangular prism
associated with
– two intersecting chords;
– two intersecting secants;
– an intersecting secant and tangent;
– two intersecting tangents; and
– central and inscribed angles.
Textbook Resources
Chapter 12 & additional
resources
Resources/Lessons
 Calculate the area of a sector and the length of an arc of
a circle, using proportions.
 Solve real-world problems associated with circles, using
properties of angles, lines, and arcs.
 Verify properties of circles, using deductive reasoning,
algebraic, and coordinate methods.
Dates
Standards/Essential Questions
Essential Knowledge/Skills/Understanding
Block
Trdtl
Standard: G.12
Essential Understanding
2 days
4 days
The student, given the coordinates of
the center of a circle and a point on
the circle, will write the equation of
the circle.
 A circle is a locus of points equidistant from a given
point, the center.
Prerequisite/Extension SOL
6.10 a) define π; b) solve practical problems
w/circumference/area of circle; c) solve
practical problems involving area and
perimeter given radius/diameter; d)
describe/determine volume/surface area of
rectangular prism
 Standard form for the equation of a circle is
 x  h   y  k 
2
2
 r 2 , where the coordinates of the
center of the circle are ( h, k ) and r is the length of the
radius.
Resources
Key Vocabulary
Standard Form for the Equation
of a Circle
DOE Lesson Plans
Equations of Circles
Textbook Resources
Chapter 12 & additional
resources
 The circle is a conic section.
Resources/Lessons
Circle Match Game
Essential Knowledge/Skills
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
Dates
Block
Trdtl
4 days
8 days
Standards/Essential Questions
Standard: G.13
The student will use formulas for
surface area and volume of threedimensional objects to solve realworld problems.

Identify the center, radius, and diameter of a circle
from a given standard equation.

Use the distance formula to find the radius of a circle.

Given the coordinates of the center and radius of the
circle, identify a point on the circle.

Given the equation of a circle in standard form,
identify the coordinates of the center and find the
radius of the circle.

Given the coordinates of the endpoints of a diameter,
find the equation of the circle.

Given the coordinates of the center and a point on the
circle, find the equation of the circle.

Recognize that the equation of a circle of given center
and radius is derived using the Pythagorean Theorem.†
Essential Knowledge/Skills/Understanding
Essential Understanding
 The surface area of a three-dimensional object is the
sum of the areas of all its faces.
Prerequisite/Extension SOL
 The volume of a three-dimensional object is the number
of unit cubes that would fill the object.
7.5 a) describe volume/surface area
of cylinders; b) solve practical
problems involving volume/surface
area of rect. prims and cylinders; c)
describe how changes in measured
attribute affects volume/surface area
Essential Knowledge/Skills
8.7 a) investigate/solve practical
 Find the total surface area of cylinders, prisms,
pyramids, cones, and spheres, using the appropriate
Resources
Key Vocabulary
DOE Lesson Plans
Surface Area & Volume
Textbook Resources
Chapter 11: 11.1 – 11.5
Resources/Lessons
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
problems involving volume/surface
area of prisms, cylinders, cones,
pyramids; b) describe how changes in
measured attribute affects
volume/surface area
8.9 construct a 3‐D model given top
or bottom/side/front views
formulas.
 Calculate the volume of cylinders, prisms, pyramids,
cones, and spheres, using the appropriate formulas.
 Solve problems, including real-world problems,
involving total surface area and volume of cylinders,
prisms, pyramids, cones, and spheres as well as
combinations of three-dimensional figures.
 Calculators may be used to find decimal approximations
for results.
Dates
Block
Trdtl
1 day
1½ days
Standards/Essential Questions
Essential Knowledge/Skills/Understanding
Standard: G.14
Essential Understanding
The student will use similar geometric
objects in two- or three-dimensions to
a) compare ratios between side
lengths, perimeters, areas, and
volumes;
b) determine how changes in one or
more dimensions of an object
affect area and/or volume of the
object;
c) determine how changes in area
and/or volume of an object affect
one or more dimensions of the
object; and
d) solve real-world problems about
 A change in one dimension of an object results in
predictable changes in area and/or volume.
 A constant ratio exists between corresponding lengths
of sides of similar figures.
 Proportional reasoning is integral to comparing attribute
measures in similar objects.
Resources
Key Vocabulary
DOE Lesson Plans
Similar Solids & Proportional
Reasoning
Textbook Resources
Chapter 11:11.6
Resources/Lessons
Essential Knowledge/Skills
 Compare ratios between side lengths, perimeters,
BEDFORD COUNTY PUBLIC SCHOOLS
Geometry Curriculum Guide
similar geometric objects.
Prerequisite/Extension SOL
7.5 a) describe volume/surface area
of cylinders; b) solve practical
problems involving volume/surface
area of rect. prims and cylinders; c)
describe how changes in measured
attribute affects volume/surface area
8.7 a) investigate/solve practical
problems involving volume/surface
area of prisms, cylinders, cones,
pyramids; b) describe how changes in
measured attribute affects
volume/surface area
areas, and volumes, given two similar figures.
 Describe how changes in one or more dimensions affect
other derived measures (perimeter, area, total surface
area, and volume) of an object.
 Describe how changes in one or more measures
(perimeter, area, total surface area, and volume) affect
other measures of an object.
 Solve real-world problems involving measured attributes
of similar objects.
Performance Task must be completed and graded on rubric by the end of Quarter 4
Sample Performance Tasks: (Exemplars)
 Now That’s a Lot of Hot Air
 Truck That Tuna
 Speeding Tires