Geometry Curriculum Guide Page 1
Geometry – At a Glance
Approximate Beginning Date – Test Date Chapters to Cover and 9 Weeks calendar dates
1st 9 Weeks August 19th – October 16th
August 19th – September 3rd Ch 1: Essentials of Geometry
September 4th – September 21st Ch 2: Reasoning and Proof
September 21st – October 1st Ch 3: Parallel and Perpendicular Lines
October 2nd – October 20th (2 pays in to 2nd 9 weeks) Ch 4: Congruent Triangles
2nd 9 Weeks October 19th – December 4th
October 21st – November 4th Ch 5: Relationships within Triangles
November 5th – November 13th Ch 6: Similarity
November 16th – December 4th Ch 7: Right Triangles and Trigonometry
December 7th, begin review for Fall Exam, Semester ends on December 18th
3rd 9 Weeks January 1st – March 11th
January 5th – January 25th Ch 8: Quadrilaterals
January 26th – February 24th Ch 9: Properties of Transformations
February 25th – March 10th Ch 10: Properties of Circles
March 11th – Pi Day
4th 9 Weeks March 21st – Mary 31st
The beginning of the 4th 9 weeks will be used as time to complete concepts if we get behind in the other 9 weeks.
March 21st – April 8th Ch 11: Measuring Length and Area
April 11th – April 29th Ch 12: Surface Area and Volume of Solids
After chapter 12, use the remainder of the year for review for the final, SAT practice, and activities.
In Geometry, students will develop reasoning and problem solving skills as they study topics such as congruence and similarity, and
apply properties of lines, triangles, quadrilaterals, and circles. Students will also develop problem solving skills by using length, perimeter,
Geometry Curriculum Guide Page 2
area, circumference, surface area, and volume to solve real-world problems.
Included in the following information are the key concepts students will learn throughout this course and the resources, materials, and
activities that will enhance this learning experience. The concepts for this course also include information that students will be tested over on
standardized tests, such as the SAT and the ITBS. Also included is an assessment stem for both low, medium, and high level questions. To
show complete mastery, a student would be able to answer all three levels of questioning.
Ongoing
Concepts Unit and Standard Key Understanding Resources, Materials,
and Activities
Assessment Stem
N-Q 1: Use units as a way to
understand problems and to guide
the solution of multi-step problems;
choose and interpret units
consistently in formulas; choose
and interpret the scale and the
origin in graphs and data displays.
-use units to aid in
solving word problems
and in creating and
reading graphs/data
displays
-convert units when
appropriate
R: Geometry textbook L: using units in solutions when
conversions are not necessary
M/H: use conversions in order to
determine a solution and understand
when units are squared (area) or
cubed (volume)
N-Q 2: Define appropriate
quantities for the purpose of
descriptive modeling.
-solve various real-
world word problems
R: Geometry textbook L/M/H: be able to solve many kinds
of word problems at various levels
N-Q 3: Choose a level of accuracy
appropriate to limitations on
measurement when reporting
quantities.
-determine the accuracy
and unit necessary
when answering word
problems
R: Geometry textbook L/M/H: understand the importance of
units and rounding in solutions
G-MG 1: Use geometric shapes,
their measures, and their properties
to describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder)
-solve various real-
world word problems
R: Geometry textbook L/M/H: be able to solve many kinds
of word problems at various levels
G-MG 3: Apply geometric methods
to solve design problems (ex:
designing an object or structure to
satisfy physical constraints or
minimize cost; working with
typographic grid systems based on
ratios).
-apply the properties of
geometric figures to
solve word problems
R: Geometry textbook L: applying basic geometric figures
(lines, points)
M: apply 2d polygons
H: apply 3d figures
Geometry Curriculum Guide Page 3
1st 9
Weeks Unit 1: Essentials of Geometry Key Understanding Resources, Materials,
and Activities
Assessment Stem
Wed, Aug
19
1st day of school: class structure and
calculator check out
M: class structure page,
calculator check out sheet
Wed, Aug
19
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
-how/why geometry
was developed
-historical figures: the
Greeks, Euclid
-define point, line, and
plane (undefined terms)
-identify and name
figures: points, lines,
planes, segments, rays,
opposite rays
-identify intersections
-sketch intersections
R: Internet sources:
enotes.com, about.com
R: Geometry textbook
chapter 1.1, Painless
Geometry,
www.classzone.com
PowerPoint
A: identify points, lines,
planes and their
intersections in the
classroom
L: Name the points, lines, planes, etc.
given the figure.
M: Given the figure, is there more
than one way to name the lines,
planes, etc.?
H: Tell if the following situation is
possible, if so, make a sketch: Three
planes intersect in one line.
Thurs,
Aug 20
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
-use graphing to
represent points, lines,
etc., “algebra review”
from pg. 7
-understand measurable
versus non-measurable
figures
-”postulates”:
postulates vs. theorems,
Ruler Postulate,
Segment Addition
Postulate
-”congruent”
-introduce String Art
project
R: Geometry textbook
chapter 1.1, 1.2
M: graph paper
L: Plot points to create a segment.
M: Plot points to create a segment.
Find the length and midpoint of the
segment. Explain why a segment is
measurable, but a line or ray is non-
measurable.
H: Plot points to create a line or ray.
Extend the line or ray so that it
maintains proper slope.
Fri, Aug Project shows the tangible String Art Project: A: String Art Project
Geometry Curriculum Guide Page 4
21 relationship between points, lines,
and planes and how they are used to
construct 3d shapes and objects
choose patterns and
string, begin project in
class, project due on
Monday Aug 24
M: back boards, nails,
string, patterns,
Mon, Aug
24
This section defines bisectors in
order to:
G-CO 9: Prove theorems about
lines and angles. Theorems include:
vertical angles are congruent; when
a transversal crosses parallel lines,
alternate interior angles are
congruent and corresponding angles
are congruent; points on a
perpendicular bisector of a line
segment are exactly those
equidistant from the segment's
endpoints.
-define: midpoint,
bisector
-understand there is
only one midpoint, but
many kinds of bisectors
-finding segment
lengths using bisectors
-Midpoint Formula
-Distance Formula
R: Geometry textbook
chapter 1.3
L: Use the formula to find the
midpoint of a segment given the
endpoints./ Measure the length of a
segment.
M:Given one endpoint and the
midpoint, find the other endpoint./
Use the Segment Addition Postulate
to find the length of a segment.
H: Use the midpoint formula and the
segment addition postulate to
determine lengths of several collinear
segments using variables and
algebraic equations.
Tues,
Aug 25
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
-parts of an angle
-naming angles
-measuring angles,
using a protractor
-classifying angles
-red square to mark
right angles
-Angle Addition
Postulate
-angle bisectors,
congruent angles
R: Geometry textbook
chapter 1.4
M: protractors
L: Given the angle measure, state
whether the angle is acute, right, or
obtuse.
M: Use the protractor to measure the
angle, state whether the angle is acute,
right or obtuse, and correctly name
the angle.
H: Use the angle addition postulate to
find angle measures using algebraic
equations.
Wed, Aug
26
G-CO 12: Make formal geometric
constructions with a variety of tools
and methods (compass and
straightedge, string, reflective
devices, paper folding, dynamic
-construct segments and
angles
R: Geometry textbook pg.
33-34
M: protractor, compass
L/M/H: use a compass and ruler to
copy and bisect segments and angles
Geometry Curriculum Guide Page 5
geometric software, etc.). Copying
a segment; copying an angle;
bisecting a segment; bisecting an
angle; constructing perpendicular
lines, including the perpendicular
bisector of a line segment; and
constructing a line parallel to a
given line through a point not on
the line.
Thurs,
Aug 27
This section defines types of angles
in order to:
G-CO 9: Prove theorems about
lines and angles. Theorems include:
vertical angles are congruent; when
a transversal crosses parallel lines,
alternate interior angles are
congruent and corresponding angles
are congruent; points on a
perpendicular bisector of a line
segment are exactly those
equidistant from the segment's
endpoints.
-identify and apply
types of angles:
complementary,
supplementary,
adjacent, vertical, and
linear pair
-interpreting from a
diagram, what you can
and cannot conclude
R: Geometry textbook
chapter 1.5
L: identify types of angles
M: For all types of angles, when given
one measure find the measure of
another
H: use equations to find angle
measures
Fri, Aug
28
This section classifies polygons in
order to:
G-MG 1: Use geometric shapes,
their measures, and their properties
to describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder)
-define polygon, parts
of a polygon
-convex vs concave
polygons
-classify polygons
-define equilateral,
equiangular, and regular
-find side lengths in
regular polygons
Geometry textbook
chapter 1.6
L: classify polygons
M: identify convex vs concave
H: use equations to find side lengths
Mon, Aug
31
G-GPE 7: Use coordinates to
compute perimeters of polygons
and areas of triangles and
-find perimeter,
circumference, and area
of squares, rectangles,
Geometry textbook
chapter 1.7
L: find area and perimeter of all
polygons when given measurements
M: find appropriate lengths to find
Geometry Curriculum Guide Page 6
rectangles, e.g., using the distance
formula
triangles, and circles;
this does NOT include
composite polygons
-solving multi-step
problems
-finding unknown
lengths, solving for a
variable in a formula
area and perimeter of all polygons
H: use distance formula to find area
and perimeter
Review on Tues, Sept 1 and Wed,
Sept 2
Test on Thurs, Sept 3
1st 9
Weeks Unit 2: Reasoning and Proof Key Understanding Resources, Materials,
and Activities
Assessment Stem
Fri, Sept
4
Inductive reasoning will prepare
students for proofs, such as those
given in G-CO 6, 7, and 8.
-define inductive
reasoning
-visual patterns
-number patterns
-Fibonacci Sequence
-make and test
conjectures
-finding
counterexamples
R: Geometry textbook
chapter 2.1
L: Given the description of a pattern
write/sketch the next figure or
number.
M: Describe the pattern and
write/sketch the next figure or
number.
H: Make and test a conjecture relating
to a group of numbers, and explain
your results. Ex: Make and test a
conjecture about the product of any
two odd numbers.
Tues,
Sept 8
-Fibonacci Sequence:
its history and
importance, and how it
applies in nature
R: United Streaming
video: Patterns,
Symmetry and Beauty
L: Given the description of the
Fibonacci Sequence, give the next
number. List examples of where it
appears in nature.
M: Describe the pattern of the
Fibonacci Sequence and give the next
number. Retell the history of its
creation and where it appears in
nature.
Geometry Curriculum Guide Page 7
H: Explain the creation of the
Fibonacci Sequence from the view of
Fibonacci during the period. How did
affect their understanding of the
world? Apply this idea to
Theology/Creation.
Wed,
Sept 9
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
-analyze conditional
statements and identify
the hypothesis and
conclusion
-negation of statements
-write the converse,
inverse, and
contrapositive
-”good” definitions,
perpendicular lines
-biconditional
statements
R: Geometry textbook
chapter 2.2
L: Identify the hypothesis and
conclusion in a conditional statement.
M: Rewrite a conditional statement in
if-then form. Determine if the
conditional statement and its negation
are true of false. Write the converse,
inverse, and contrapositive of the
conditional statement.
H: Using a conditional statement and
its converse, determine if a definition
is a 'good' definition.
Thurs,
Sept 10
Deductive reasoning will prepare
students for proofs, such as those
given in G-CO 6, 7, and 8.
-define deductive
reasoning
-Law of Detachment
-Law of Syllogism
-identify whether
inductive or deductive
reasoning is used
-reasoning from a graph
R: Geometry textbook
chapter 2.3
L: Make a valid conclusion given a
situation. Ex: Mary goes to the
movies every Friday and Saturday.
Today is Friday. What is the
conclusion?
M: Given true statements, write a new
conditional statement.
H: Understand the difference between
inductive and deductive reasoning.
Use inductive and deductive
reasoning to show a conjecture is true.
Fri, Sept
11
During class students will be able to interact with a variety of
logic puzzles including: Enigmathics, traditional logic
puzzles, Magnatiles, toothpick puzzles, 3d puzzles,
pentominoes
A: logic puzzles
Mon, Interpreting diagrams will prepare -review of Postulates 1- R: Geometry textbook L: Identify postulates from a diagram.
Geometry Curriculum Guide Page 8
Sept 14 students for proofs, such as those
given in G-CO 6, 7, and 8.
11
-identify postulates
from a diagram
-use information to
sketch a diagram
-what can and cannot be
assumed from a
diagram, interpreting 3d
diagrams
chapter 2.4 M: Use a diagram to determine if
statements are true or false.
H Use a diagram to write example
statements of postulates.
Tues,
Sept 15
A-REI 1: Explain each step in
solving a simple equation as
following from the equality of
numbers asserted at the previous
step, starting from the assumption
that the original equation has a
solution. Construct a viable
argument to justify a solution
method.
-algebraic properties of
equality, including
distributive properties
-apply the algebraic
properties to steps of
solving an equation
-Reflexive, Symmetric,
and Transitive
Properties
-writing two-column
proofs when solving
equations
R: Geometry textbook
chapter 2.5
L/M: Complete a two-column proof,
to prove an algebraic expression.
H: Complete a two-column proof,
using algebraic expressions in a
geometric figure. Ex: Algebraic
expressions for angle measures 7x+22
and 4x-8 and the sum of the angles is
124. Prove the value of x.
Wed,
Sept 16
G-CO 9: Prove theorems about
lines and angles. Theorems include:
vertical angles are congruent; when
a transversal crosses parallel lines,
alternate interior angles are
congruent and corresponding angles
are congruent; points on a
perpendicular bisector of a line
segment are exactly those
equidistant from the segment's
endpoints.
-Reflexive, Symmetric,
and Transitive
properties applied to
segments and angles
-write two-column
proofs involving
segments and angles
R: Geometry textbook
chapter 2.6
L: Complete a fill-in-the blank two-
column proof.
M: Complete a matching two-column
proof.
H: Write a two-column proof.
Thurs,
Sept 17
G-CO 9: Prove theorems about
lines and angles. Theorems include:
-Right Angles
Congruence Theorem
R: Geometry textbook
chapter 2.7
L: Complete a fill-in-the blank two-
column proof.
Geometry Curriculum Guide Page 9
vertical angles are congruent; when
a transversal crosses parallel lines,
alternate interior angles are
congruent and corresponding angles
are congruent; points on a
perpendicular bisector of a line
segment are exactly those
equidistant from the segment's
endpoints.
-Congruent
Complements Theorem
-Congruent
Supplements Theorem
-Linear Pair Postulate
-Vertical Angles
Congruence Theorem
-use these theorems and
postulates to find angle
measures and prove
they are correct
M: Complete a matching two-column
proof.
H: Write a two-column proof.
Assign Ch 2 take home test on Fri,
Sept 18, test due on Mon, Sept 21
1st 9
Weeks Unit 3: Parallel and
Perpendicular Lines
Key Understanding Resources, Materials,
and Activities
Assessment Stem
Mon,
Sept 21
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
-identify parallel lines,
skew lines, and parallel
planes in 3d figures
-Parallel and
Perpendicular
Postulates
-angles formed by
transversals
R: Geometry textbook
chapter 3.1
L/M/H: Identify pairs of angles
formed by a transversal. Identify
parallel lines, skew lines, and parallel
planes in 3d figures
Tues,
Sept 22-
Wed,
Sept 23
G-CO 9: Prove theorems about
lines and angles. Theorems include:
vertical angles are congruent; when
a transversal crosses parallel lines,
alternate interior angles are
congruent and corresponding angles
are congruent; points on a
perpendicular bisector of a line
segment are exactly those
-find angle measures
given parallel lines and
a transversal
-complete simple proofs
involving parallel lines
and transversals
R: Geometry textbook
chapter 3.2, 3.3
L: Find angle measures involving
parallel lines and transversals.
M/H: Complete proofs involving
parallel lines and transversals.
Geometry Curriculum Guide Page 10
equidistant from the segment's
endpoints.
Thurs,
Sept 24
G-GPE 5: Prove the slope criteria
for parallel and perpendicular lines
and use them to solve geometric
problems (e.g., find the equation of
a line parallel or perpendicular to a
given line that passes through a
given point).
-what is slope?
-slope formula and
rise/run
-identify negative,
positive, zero, and
undefined slope
-find the slopes of lines
-slopes of parallel and
perpendicular lines
-draw a line
perpendicular to
another line
R: Geometry textbook
chapter 3.4
L: Identify lines as having positive
slope, negative slope, no slope, or
undefined slope.
M: Find the slope of a line given two
points or the line on a graph.
H: Given the slope and one
coordinate, find the missing
coordinate.
Fri, Sept
25
G-GPE 5: Prove the slope criteria
for parallel and perpendicular lines
and use them to solve geometric
problems (ex: find the equation of a
line parallel or perpendicular to a
given line that passes through a
given point).
A-CED 2: Create equations in two
or more variables to represent
relationships between quantities;
graph equations on coordinate axes
with labels and scales.
A-REI 10: Understand that the
graph of an equation in two
variables is the set of all its
solutions plotted in the coordinate
plane, often forming a curve (which
could be a line).
-slope-intercept form
-write equations of lines
from a graph, and for
parallel and
perpendicular lines
-standard form
-graphing lines in
standard form
-for 3.6, go over
theorems about
perpendicular lines
-do some of the 3.6
exercises together
R: Geometry textbook
chapter 3.5, 3.6
L: Write the equation of a line and
graph the line.
M: Show lines are parallel or
perpendicular by using slope.
H: Graph two perpendicular lines.
Understand perpendicular lines can be
used to form a right triangle.
Geometry Curriculum Guide Page 11
Assign Review on Mon, Sept 28
Go over review on Tues, Sept 29
Test on Wed, Sept 30
Thurs,
Oct 1
G-CO 12: Make formal geometric
constructions with a variety of tools
and methods (compass and
straightedge, string, reflective
devices, paper folding, dynamic
geometric software, etc.). Copying
a segment; copying an angle;
bisecting a segment; bisecting an
angle; constructing perpendicular
lines, including the perpendicular
bisector of a line segment; and
constructing a line parallel to a
given line through a point not on
the line.
-construct parallel lines
-Plato and his
contributions to
constructions
R: Geometry textbook
chapter 3 (pg. 152)
M: ruler, compass
R: internet source:
http://en.wikipedia.org/wi
ki/History_of_geometry#
Plato
L/M/H: use a compass and ruler to
create parallel lines
1st 9
Weeks Unit 4: Congruent Triangles Key Understanding Resources, Materials,
and Activities
Assessment Stem
Fri, Oct 2 G-CO 10: Prove theorems about
triangles. Theorems include:
measures of interior angles of a
triangle sum to 180 degrees; base
angles of isosceles triangles are
congruent; the segment joining
midpoints of two sides of a triangle
is parallel to the third side and half
the length; the medians of a triangle
meet at a point.
-classify triangles by
angles and sides
-interior and exterior
angles of triangles
-finding angle measures
-corollary to the
triangle sum theorem
R: Geometry textbook
chapter 4.1
L: What is the sum of the angles of a
triangle?
M: When given two angle measures
of a triangle, find the measure of the
third angle.
H: Given algebraic equations for
angle measures in a triangle, find the
measure of each angle.
Mon, Oct
5
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
-what are congruent
figures?
-writing a congruence
statement
R: Geometry textbook
chapter 4.2
L: Determine if triangles are
congruent when given all
measurements.
M/H: Determine if triangles are
Geometry Curriculum Guide Page 12
-identify corresponding
parts
-third angle theorem
-congruent parts of
congruent triangles
-CPCTC
congruent when not given all
measurements
Tues, Oct
6
This activity will lead to proving
congruence by SSS.
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
-investigate triangles
and quadrilaterals to
determine how much
information is needed
to show figures are
congruent. Do the
Explore 1 and 2
together, Draw
Conclusions with a
partner.
R: Geometry textbook pg.
233
A: Investigate Congruent
Figures using SSS
M: straws
L/M/H: Determine how much
information is needed to tell whether
two figures are congruent.
Wed, Oct
7
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
-SSS postulate
-determine if triangles
are congruent by SSS
-using the distance
formula for SSS
-write congruence
statements
-stability of a triangle
-watch short video over
triangles and bridges
-assign spaghetti bridge
project
R: Geometry textbook
chapter 4.3
R: short video over
triangles and bridges
A: Spaghetti Bridge
M: spaghetti, glue,
project instructions
L: Determine if figures are stable.
Determine if triangles are congruent
by SSS
M: Write congruence statements for
congruent triangles.
H: Use the distance formula to show
triangles are congruent.
Thurs,
Oct 8
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
-included angles
-SAS postulate
-define leg and
hypotenuse in right
R: Geometry textbook
chapter 4.4
L: Identify the included angle.
M: Determine if triangles are
congruent by SAS or HL.
H: Complete proofs involving SAS or
Geometry Curriculum Guide Page 13
triangles
-HL theorem
-determine if triangles
are congruent by SAS
or HL
HL.
Fri, Oct 9 G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
-ASA postulate and
AAS theorem
-define paragraph and
flow proofs (don't
necessarily do any, but
make sure they know
there are other kinds of
proofs)
-review of triangle
congruence postulates
and theorems, pg. 252
-determine if triangles
are congruent by SSS,
SAS, HL, ASA, or AAS
R: Geometry textbook
chapter 4.5
L: Determine how triangles are
congruent.
M: Use distance formula, slope
formula, and angle measurements to
show triangles congruent. (Pg. 253
#21)
H: Complete proofs involving triangle
congruence.
This section can be skipped. If it is
not skipped, apply G-SRT 5.
This section is a review
of the previous sections.
If the previous sections
are covered well, this
section can be skipped.
R: Geometry textbook
chapter 4.6
Mon, Oct
12
G-CO 10: Prove theorems about
triangles. Theorems include:
measures of interior angles of a
triangle sum to 180; base angles of
isosceles triangles are congruent;
the segment joining midpoints of
two sides of a triangle is parallel to
the third side and half the length;
the medians of a triangle meet at a
point.
-parts of an isosceles
triangle
-base angles theorem
and its converse
-corollary to the base
angles theorem and its
converse
-applying side lengths
and angle measures to
isosceles and equilateral
4.7 L: Find angle measures and side
lengths; no equations.
M/H: Find angle measures and side
lengths using equations.
Geometry Curriculum Guide Page 14
triangles
Test over 4.1-4.7:
Assign review on Tues, Oct 13
Go over review on Wed, Oct 14
Test on Thurs, Oct 15 (2nd 9 weeks grade)
Fri, Oct
16
G-CO 2: Represent transformations
in the plane using, e.g.,
transparencies and geometry
software; describe transformations
as functions that take points in the
plane as inputs and give other
points as outputs. Compare
transformations that preserve
distance and angle to those that do
not (e.g., translation versus
horizontal stretch)
G-CO 4: Develop definitions of
rotations, reflections, and
translations in terms of angles,
circles, perpendicular lines, parallel
lines, and line segments.
G-CO 5: Given a geometric figure
and a rotation, reflection, or
translation, draw the transformed
figure using, e.g., graph paper,
tracing paper, or geometry software.
Specify a sequence of
transformations that will carry a
given figure onto another.
G-CO 6: Use geometric
descriptions of rigid motions to
-transformations, image
vs pre-image
-congruence
transformations
-translate figures
-reflect figures over x
and y axis
-identify rotations
R: Geometry textbook
chapter 4.8
L: identify the type of transformation
M: use rules to perform
transformations
H: when given a transformation,
write a rule
Geometry Curriculum Guide Page 15
transform figures and to predict the
effect of a given rigid motion on a
given figure; given two figures, use
the definition of congruence in
terms of rigid motions to decide if
they are congruent.
G-CO 7: Use the definition of
congruence in terms of rigid
motions to show that two triangles
are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
G-CO 8: Explain how the criteria
for triangle congruence (ASA, SAS,
and SSS) follow from the definition
of congruence in terms of rigid
motions
Mon, Oct
19
Go over 4.8 hw, for quiz tomorrow
Break Spaghetti Bridges
test grade for 2nd 9 weeks
Tues, Oct
20
Quiz over 4.8
Finish breaking any bridges
2nd 9
Weeks Unit 5: Relationships within
Triangles
Key Understanding Resources, Materials,
and Activities
Assessment Stem
G-CO 10: Prove theorems about
triangles. Theorems include:
measures of interior angles of a
triangle sum to 180 degrees; base
angles of isosceles triangles are
congruent; the segment joining
-define midsegment
-Midsegment theorem
-placing figures in a
coordinate plane
-variable coordinates
R: Geometry textbook
chapter 5.1
L: Define midsegment.
M: Find the length of the midsegment
of a triangle.
H: Find the midsegment of a triangle
on a coordinate grid.
Geometry Curriculum Guide Page 16
midpoints of two sides of a triangle
is parallel to the third side and half
the length; the medians of a triangle
meet at a point.
G-CO 9: Prove theorems about
lines and angles. Theorems include:
vertical angles are congruent; when
a transversal crosses parallel lines,
alternate interior angles are
congruent and corresponding angles
are congruent; points on a
perpendicular bisector of a line
segment are exactly those
equidistant from the segment's
endpoints.
-perpendicular bisectors
-applying the
perpendicular bisector
theorem and its
converse
-define concurrent
-point of concurrency,
circumcenter
-locations of
circumcenters in
various types of
triangles
R: Geometry textbook
chapter 5.2
L: Find side lengths using
perpendicular bisectors; simple
equations.
M: Find side lengths using
perpendicular bisectors; complex
equations.
H: Use a ruler to find the circumcenter
of a triangle.
*there is no common core standard
to match this concept
-define angle bisector
-angle bisector theorem
and its converse
-applying the angle
bisector theorem
-point of concurrency,
incenter
R: Geometry textbook
chapter 5.3
L: Finding angle measures with angle
bisectors.
M/H: Solving word problems.
*there is no specific common core
standard to match this concept, but
understanding altitudes helps when
finding the area of a triangle:
G-GPE 7: Use coordinates to
compute perimeters of polygons
and areas of triangles and
rectangles, e.g., using the distance
formula.
-define median
-point of concurrency,
centroid
-applying the centroid
to triangles
-applying the centroid
to graphs and
coordinates
-altitudes of a triangle
-point of concurrency,
orthocenter
R: Geometry textbook
chapter 5.4
L: Find measurements of centroids
and side lengths in triangles.
M: Find centroids using coordinates
of a triangle.
H: Differentiate between
perpendicular bisectors, angle
bisectors, medians, and altitudes when
given a figure.
Geometry Curriculum Guide Page 17
-application to isosceles
triangles
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
-Triangle Inequality
theorem
- use inequalities in a
triangle (PSAT)
- understand how angle
measures relate to side
lengths (PSAT)
-hinge theorem, use
logic to determine how
changing one angle
effects another
R: Geometry textbook
chapter 5.5, 5.6
L: Understand that not all lengths will
form a triangle.
M/ H: Determine if given lengths will
form a triangle.
Find a comprehensive activity for
this chapter – no test
2nd 9
Weeks Unit 6: Similarity Key Understanding Resources, Materials,
and Activities
Assessment Stem
G-GPE 6: Find the point on a
directed line segment between two
given points that partitions the
segment in a given ratio.
-what are ratios? relate
to fractions
-simplify ratios with
like units and using
conversions
-write ratios to compare
lengths
-use ratios to find a
dimension
-extended ratios
-what is a proportion?
-solve proportions
-geometric mean, as a
specific type of
proportion
R: Geometry textbook
chapter 6.1
M: conversion list
L: Write and simplify a ratio. Solve a
proportion.
M: Use extended ratios to find angle
measures in a triangle. Solve a
proportion with algebraic equations as
factors using the distributive property
and the foil method.
H: Given the perimeter of a rectangle
and the length to width ratio, find the
length and width.
Geometry Curriculum Guide Page 18
The concept of scale leads to
understanding similarity.
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures
-properties of
proportions
-use the properties of
proportions to find side
lengths in figures
-what is scale and scale
drawings?
-scale drawings, maps
R: Geometry textbook
chapter 6.2
L: Find side lengths in figures.
M/H: Use scale and scale factors to
solve word problems.
Map Activity, Blueprint Activity
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures
-define similar,
corresponding sides and
angles
-similarity statements
-scale factor
-finding side lengths in
similar figures
-perimeters in similar
figures
-corresponding lengths
in similar polygons
R: Geometry textbook
chapter 6.3
L: Determine if figures are similar.
M: Find lengths and perimeters in
similar figures.
H: Use scale factors to find other
lengths in figures.
Scale Activity
G-SRT 3: Use the properties of
similarity transformations to
establish the AA criterion for two
triangles to be similar.
-Angles and Similar
Triangles activity, pg.
381
-AA postulate
-apply the AA postulate
-indirect measurement
R: Geometry textbook
chapter 6.4
A: Angles and Similar
Triangles, pg. 381
M: protractors, rulers
L: Determine if triangles are similar
by AA.
M: Find side lengths in similar
triangles.
H: Determine triangle similarity with
coordinates.
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures
-use the SSS and SAS
similarity theorems
-choosing a similarity
method, AA, SAS, or
SSS
R: Geometry textbook
chapter 6.5
L: Determine if triangles are similar
by SAS, SSS, or AA.
M/H: Find the scale factor and side
lengths in similar triangles.
Geometry Curriculum Guide Page 19
G-SRT 4: Prove theorems about
triangles. Theorems include: a line
parallel to one side of a triangle
divides the other two
proportionally, and conversely; the
Pythagorean Theorem proved using
triangle similarity.
-Proportionality
Theorem and its
converse
-use the proportionality
theorem to find the
length of a segment
R: Geometry textbook
chapter 6.6
L/M/H: Find segment lengths using
the proportionality theorem.
G-SRT 1: Verify experimentally the
properties of dilations given by a
center and a scale factor.
a. A dilation takes a line not
passing through the center of the
dilation to a parallel line, and leaves
a line passing through the center
unchanged.
b. The dilation of a line segment
is longer or shorter in the ratio
given by the scale factor.
G-SRT 2: Given two figures, use
the definition of similarity in terms
of similarity transformations to
decide if they are similar; explain
using similarity transformations the
meaning of similarity for triangles
as the equality of all corresponding
pairs of angles and the
proportionality of all corresponding
pairs of sides.
-define dilation, center
of dilation, and scale
factor of a dilation
-reduction vs.
enlargement
-draw dilations
-show that figures from
dilations are similar
-finding scale factor
R: Geometry textbook
chapter 6.7
L: Draw dilations.
M: Find the scale factor.
H: Determine side lengths of a
dilation.
Assign review on
Go over review on
Test on
*maybe do a project test for this
chapter instead
Geometry Curriculum Guide Page 20
2nd 9
Weeks Unit 7: Right Triangles and
Trigonometry
Key Understanding Resources, Materials,
and Activities
Assessment Stem
Understanding the Pythagorean
Theorem leads to:
G-SRT 8: Use trigonometric ratios
and the Pythagorean Theorem to
solve right triangles in applied
problems.
-apply Pythagorean
Theorem to find a
missing length
-understand the
Pythagorean Theorem
is derived from the
distance formula
-use Pythagorean
Theorem to find the
area of an isosceles
triangle
-use Pythagorean
Triples to find a
missing length
-history of Pythagoras
R: Geometry textbook
chapter 7.1
R: Internet info on
Pythagoras
L: Apply the Pythagorean Theorem to
find a missing length.
M: Find the area of an isosceles
triangle.
H: Use the distance formula and the
Pythagorean Theorem to prove/solve
a right triangle on a coordinate graph
-Pythagoras and his
contribution to
mathematics
R: United Streaming
video: Culture and Math,
Ancient Greeks
L: Name the person who contributed
to the Pythagorean Theorem.
M: Explain how the Pythagorean
Theorem would have been used
during the time of Pythagoras
H: Explain how mathematicians, like
Pythagoras, contributed to their
society and culture. How do you think
they were viewed by others?
*There is no common core standard
for this concept
-converse of the
Pythagorean Theorem
-verify right triangles
-classify triangles as
right, acute, or obtuse
R: Geometry textbook
chapter 7.2
L: Determine if triangles are right
triangles.
M: Determine if triangles are right,
acute, or obtuse.
H: Use coordinates for triangles to
classify using the distance formula.
Geometry Curriculum Guide Page 21
G-SRT 4: Prove theorems about
triangles. Theorems include: a line
parallel to one side of a triangle
divides the other two
proportionally, and conversely; the
Pythagorean theorem proved using
triangle similarity.
-identifying similar
triangles with the
altitude drawn
-using similarity and
proportions to find
lengths
-geometric mean
theorems
R: Geometry textbook
chapter 7.3
L: Write a ratio comparing lengths in
similar triangles.
M: Use proportions to find a missing
length or show triangles are similar.
Find the geometric mean given two
numbers.
H: Apply the geometric mean
theorems to triangles.
G-SRT 6: Understand that by
similarity, side ratios in right
triangles are properties of the angles
in the triangles, leading to
definitions of trigonometric ratios
for acute angles.
-apply the 45-45-90
triangle theorem
-working with square
roots
-apply the 30-60-90
triangle theorem
R: Geometry textbook
chapter 7.4, Painless
Geometry
L: Explain why some triangles are
called special right triangles.
M: Find a missing length in a special
right triangle.
H: Given a special right triangle on a
coordinate graph, be able to locate the
coordinate of a vertex.
This concept leads to:
G-SRT 8: Use trigonometric ratios
and the Pythagorean Theorem to
solve right triangles in applied
problems.
-define trigonometric
ratio
-write tangent ratios
-use tangent to find side
lengths
-combine tangent with
special right triangles
R: Geometry textbook
chapter 7.5
L: Write tangent ratios.
M: Find side lengths using tangent.
H: Use tangent to find the area of a
triangle.
G-SRT 7: Explain and use the
relationship between the sine and
cosine of complementary angles.
-define sine and cosine
ratios
-write sine and cosine
ratios
-use sine and cosine to
find side lengths
-angles of elevation and
depression
-combine sine and
cosine with special
right triangles
R: Geometry textbook
chapter 7.6
L: Write sine and cosine ratios.
M: Find side lengths using sine or
cosine.
H: Use sine and cosine to find
perimeter or area of a figure.
G-SRT 8: Use trigonometric ratios -using inverse R: Geometry textbook L: Write inverse ratios.
Geometry Curriculum Guide Page 22
and the Pythagorean Theorem to
solve right triangles in applied
problems.
trigonometric ratios to
find angle measures
-solving right triangles
chapter 7.7 M/H: Solve right triangles.
Review on
Test on
Begin Semester Review on
go over review on
3rd 9
Weeks Unit 8: Quadrilaterals Key Understanding Resources, Materials,
and Activities
Assessment Stem
This concept leads to:
G-MG 1: Use geometric shapes,
their measures, and their properties
to describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder)
-use patterns to
determine the sum of
interior angles of a
polygon
A: Investigate Angle
Sums in Polygons, pg.
506
M: straightedge
This concept leads to:
G-MG 1: Use geometric shapes,
their measures, and their properties
to describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder)
-how to name polygons
-interior angles of
polygons
-interior angles of
quadrilaterals
-find the sum of interior
angles
-find the number of
sides of a polygon
-find an unknown angle
measure
-exterior angles
theorem
R: Geometry textbook
chapter 8.1
L: Find the sum of the interior angles
of a polygon.
M: Solve equations using the interior
and exterior angles of polygons.
H: Find the number of sides when
given the sum of the interior angles.
G-CO 11: Prove theorems about
parallelograms. Theorems include:
opposite sides are congruent,
opposite angles are congruent, the
-define parallelogram
-properties of
parallelograms
-use the properties of
R: Geometry textbook
chapter 8.2, 8.3
M: quadrilateral
L/M/H: Use the properties of
parallelograms to find side lengths
and angle measures.
Geometry Curriculum Guide Page 23
diagonals of a parallelogram bisect
each other, and conversely,
rectangles are parallelograms with
congruent diagonals.
parallelograms
-show that a
quadrilateral is a
parallelogram
properties chart
A: begin a Venn diagram
for quadrilaterals
G-GPE 4: Use coordinates to prove
simple geometric theorems
algebraically. For example, prove or
disprove that a figure defined by
four given points in the coordinate
plane is a rectangle; prove or
disprove that the point (1, √3) lies
on the circle centered at the origin
and containing the point (0, 2).
-properties of
rhombuses, rectangles,
and squares
R: Geometry textbook
chapter 8.4
M: quadrilateral
properties chart
A: Venn diagram
for quadrilaterals
L/M/H: Use the properties of
rhombuses, rectangles, and squares to
find side lengths and angle measures.
G-GPE 4: Use coordinates to prove
simple geometric theorems
algebraically. For example, prove or
disprove that a figure defined by
four given points in the coordinate
plane is a rectangle; prove or
disprove that the point (1, √3) lies
on the circle centered at the origin
and containing the point (0, 2).
-properties of
trapezoids and isosceles
trapezoids
-midsegments of
trapezoids
-properties of kites
R: Geometry textbook
chapter 8.5
M: quadrilateral
properties chart
A: Venn diagram
for quadrilaterals
L/M/H: Use the properties of
trapezoids and kites to find side
lengths and angle measures.
G-MG 1: Use geometric shapes,
their measures, and their properties
to describe objects (e.g., modeling a
tree trunk or a human torso as a
cylinder)
-identify quadrilaterals
given various properties
R: Geometry textbook
chapter 8.6
M: quadrilateral
properties chart,
properties chart for
homework
A: Venn diagram
for quadrilaterals
L/M/H: Identify polygons based on
properties, such as angle measures
and side lengths given.
Assign review on
Go over review on
Geometry Curriculum Guide Page 24
Test on
Create 3d drawings -create orthographic
and isometric drawings
R: Geometry textbook pg.
550-551
M: graph paper, isometric
dot paper
3rd 9
Weeks Unit 9: Properties of
Transformations
Key Understanding Resources, Materials,
and Activities
Assessment Stem
N-VM 1: Recognize vector
quantities as having both magnitude
and direction. Represent vector
quantities by directed line
segments, and use appropriate
symbols for vectors and their
magnitudes (e.g., v, |v|, ||v||, v).
G-CO 2: Represent transformations
in the plane using, e.g.,
transparencies and geometry
software; describe transformations
as functions that take points in the
plane as inputs and give other
points as outputs. Compare
transformations that preserve
distance and angle to those that do
not (e.g., translation versus
horizontal stretch)
G-CO 4: Develop definitions of
rotations, reflections, and
translations in terms of angles,
circles, perpendicular lines, parallel
lines, and line segments.
-review
transformations, image
vs. pre-image
-prime notation
-translate figures
-define isometry
(congruence
transformation)
-write a translation rule
-define vectors, and
parts of vectors,
component form
-identify vector
components
-use vectors to translate
figures
R: Geometry textbook
chapter 9.1
L: Translate a figure.
M: Write the rule for a translation.
H: Use translations and vectors to
solve word problems, and solve for
side lengths and angle measures.
Geometry Curriculum Guide Page 25
G-CO 5: Given a geometric figure
and a rotation, reflection, or
translation, draw the transformed
figure using, e.g., graph paper,
tracing paper, or geometry software.
Specify a sequence of
transformations that will carry a
given figure onto another.
G-CO 6: Use geometric
descriptions of rigid motions to
transform figures and to predict the
effect of a given rigid motion on a
given figure; given two figures, use
the definition of congruence in
terms of rigid motions to decide if
they are congruent.
G-CO 7: Use the definition of
congruence in terms of rigid
motions to show that two triangles
are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
G-CO 8: Explain how the criteria
for triangle congruence (ASA, SAS,
and SSS) follow from the definition
of congruence in terms of rigid
motions
N-VM 6: Use matrices to represent
and manipulate data, e.g., to
represent payoffs or incidence
relationships in a network
-define matrix and
dimensions
-represent figures using
matrices
R: Geometry textbook
chapter 9.2
Geometry Curriculum Guide Page 26
N-VM 8: Add, Subtract, and
multiply matrices of appropriate
dimensions
N-VM 12: Work with 2x2 matrices
as transformations of the plane, and
interpret the absolute value of the
determinant in terms of area.
G-CO 2: Represent transformations
in the plane using, e.g.,
transparencies and geometry
software; describe transformations
as functions that take points in the
plane as inputs and give other
points as outputs. Compare
transformations that preserve
distance and angle to those that do
not (e.g., translation versus
horizontal stretch)
G-CO 5: Given a geometric figure
and a rotation, reflection, or
translation, draw the transformed
figure using, e.g., graph paper,
tracing paper, or geometry software.
Specify a sequence of
transformations that will carry a
given figure onto another.
G-CO 6: Use geometric
descriptions of rigid motions to
transform figures and to predict the
effect of a given rigid motion on a
-adding and subtracting
matrices
-represent translations
using matrices
-multiplying matrices
(this will be applied to
reflections in the next
section)
Geometry Curriculum Guide Page 27
given figure; given two figures, use
the definition of congruence in
terms of rigid motions to decide if
they are congruent.
G-CO 7: Use the definition of
congruence in terms of rigid
motions to show that two triangles
are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
G-CO 3: Given a rectangle,
parallelogram, trapezoid, or regular
polygon, describe the rotations and
reflections that carry it onto itself.
G-CO 4: Develop definitions of
rotations, reflections, and
translations in terms of angles,
circles, perpendicular lines, parallel
lines, and line segments.
G-CO 5: Given a geometric figure
and a rotation, reflection, or
translation, draw the transformed
figure using, e.g., graph paper,
tracing paper, or geometry software.
Specify a sequence of
transformations that will carry a
given figure onto another.
G-CO 6: Use geometric
descriptions of rigid motions to
transform figures and to predict the
-define line or
reflection
-graph reflections in
horizontal and vertical
lines
-graph reflections in
y=x and -x
-reflection rules
-do a double reflection
example
-reflections with
matrices
R: Geometry textbook
chapter 9.3
L: Graph reflections in the x and y
axis.
M: Graph reflections in y=x and y=-x
H: Graph reflections using matrices.
Geometry Curriculum Guide Page 28
effect of a given rigid motion on a
given figure; given two figures, use
the definition of congruence in
terms of rigid motions to decide if
they are congruent.
G-CO 7: Use the definition of
congruence in terms of rigid
motions to show that two triangles
are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
N-VM 10: Understand that the zero
and identity matrices play a role in
matrix addition and multiplication
similar to the role of 0 and 1 in the
real numbers. The determinant of a
square matrix is nonzero if and only
if the matrix has a multiplicative
inverse.
G-CO 3: Given a rectangle,
parallelogram, trapezoid, or regular
polygon, describe the rotations and
reflections that carry it onto itself.
G-CO 4: Develop definitions of
rotations, reflections, and
translations in terms of angles,
circles, perpendicular lines, parallel
lines, and line segments.
G-CO 5: Given a geometric figure
and a rotation, reflection, or
-review definitions
rotation, center of
rotation, and angle of
rotation
-draw a rotation with a
protractor
-rules for rotations
-rotate a figure using
the rules
-rotation rules using
matrices
R: Geometry textbook
chapter 9.4
M: protractors
L: Rotate using the rules.
M/H: Rotate using a protractor.
Geometry Curriculum Guide Page 29
translation, draw the transformed
figure using, e.g., graph paper,
tracing paper, or geometry software.
Specify a sequence of
transformations that will carry a
given figure onto another.
G-CO 6: Use geometric
descriptions of rigid motions to
transform figures and to predict the
effect of a given rigid motion on a
given figure; given two figures, use
the definition of congruence in
terms of rigid motions to decide if
they are congruent.
G-CO 7: Use the definition of
congruence in terms of rigid
motions to show that two triangles
are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
G-CO 3: Given a rectangle,
parallelogram, trapezoid, or regular
polygon, describe the rotations and
reflections that carry it onto itself.
G-CO 5: Given a geometric figure
and a rotation, reflection, or
translation, draw the transformed
figure using, e.g., graph paper,
tracing paper, or geometry software.
Specify a sequence of
transformations that will carry a
-define composition of
transformations
-define glide reflection
-find the image of a
glide reflection
-perform various types
of composition of
transformations
R: Geometry textbook
chapter 9.5
L: Perform a composition of
transformations.
M/H: Describe, write a rule for, a
composition of transformations.
Geometry Curriculum Guide Page 30
given figure onto another.
G-CO 6: Use geometric
descriptions of rigid motions to
transform figures and to predict the
effect of a given rigid motion on a
given figure; given two figures, use
the definition of congruence in
terms of rigid motions to decide if
they are congruent.
G-CO 7: Use the definition of
congruence in terms of rigid
motions to show that two triangles
are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
Work on Tessellation project on
Project due on
-use tessellations as a
way to perform a
composition of
transformations
R: Geometry textbook pg
616-618
M: instructions packet
G-CO 4: Develop definitions of
rotations, reflections, and
translations in terms of angles,
circles, perpendicular lines, parallel
lines, and line segments.
-define line symmetry
and line of symmetry
-identify lines of
symmetry (ex: circles)
-define rotational
symmetry and center of
symmetry
-identify rotational
symmetry
R: Geometry textbook
chapter 9.6
L: Be able to identify line symmetry.
M/H: Be able to identify line and
rotational symmetry.
N-VM 7: Multiply matrices by
scalars to produce new matrices,
e.g., as when all of the payoffs in a
-review definition of
dilation, reduction, and
enlargement
R: Geometry textbook
chapter 9.7
L: Perform dilations
M: Determine the scale factor of
dilations.
Geometry Curriculum Guide Page 31
game are doubled.
G-SRT 1: Verify experimentally the
properties of dilations given by a
center and a scale factor.
a. A dilation takes a line not
passing through the center of the
dilation to a parallel line, and leaves
a line passing through the center
unchanged.
b. The dilation of a line segment
is longer or shorter in the ratio
given by the scale factor.
-identify dilations
-draw dilations
-scalar multiplication
-apply scalar
multiplication to
dilations
H: Perform a composition of
transformations that includes
dilations.
Assign review on
Go over review on
Test on
3rd 9
Weeks Unit 10: Properties of Circles Key Understanding Resources, Materials,
and Activities
Assessment Stem
G-CO 1: Know precise definitions
of angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line,
and distance around a circular arc.
G-C 1: Prove that all circles are
similar.
G-C 2: Identify and describe
relationships among inscribed
angles, radii, and chords. Include
the relationship between central,
inscribed, and circumscribed
angles; inscribed angles on a
-define and identify
parts of a circle
-radius and diameter
relationship
-coplanar circles
-common tangents
-verify a tangent to a
circle
-find the radius of a
circle
-property of tangents
with a common external
point
R: Geometry textbook
chapter 10.1
M: circle notes
L: Identify parts of a circle.
M/H: Use equations to find lengths of
tangents.
Geometry Curriculum Guide Page 32
diameter are right angles; the radius
of a circle is perpendicular to the
tangent where the radius intersects
the circle.
G-C 2: Identify and describe
relationships among inscribed
angles, radii, and chords. Include
the relationship between central,
inscribed, and circumscribed
angles; inscribed angles on a
diameter are right angles; the radius
of a circle is perpendicular to the
tangent where the radius intersects
the circle.
-define central angle,
minor arc, major arc,
and semicircle
-naming arcs
-measures of arcs
-Arc Addition postulate
-congruent circles and
congruent arcs
R: Geometry textbook
chapter 10.2
L: Identify arcs as minor, major, or
semicircle.
M: Find measures of a few arcs in a
circle.
H: Find measures of many arcs in a
circle.
G-C 2: Identify and describe
relationships among inscribed
angles, radii, and chords. Include
the relationship between central,
inscribed, and circumscribed
angles; inscribed angles on a
diameter are right angles; the radius
of a circle is perpendicular to the
tangent where the radius intersects
the circle.
-use congruent chords
to find arc measures
-bisecting arcs
-how to use
perpendicular bisectors
in circles
-using a diameter with a
chord
-chords equidistant
from the center of a
circle
R: Geometry textbook
chapter 10.3
L: Know which chords are congruent
in a circle.
M/H: Use equations to determine
lengths of chords.
G-CO 13: Construct an equilateral
triangle, a square, and a regular
hexagon inscribed in a circle.
G-C 2: Identify and describe
relationships among inscribed
angles, radii, and chords. Include
the relationship between central,
inscribed, and circumscribed
-define inscribed angle
and intercepted arc
-use inscribed angles to
find angle and arc
measures
-define inscribed
polygon and
circumscribed circle
-inscribed quadrilaterals
R: Geometry textbook
chapter 10.4
L: Determine arc measures.
M: Determine angles measures of
inscribed polygons.
H: Construct inscribed polygons.
Geometry Curriculum Guide Page 33
angles; inscribed angles on a
diameter are right angles; the radius
of a circle is perpendicular to the
tangent where the radius intersects
the circle.
G-C 3: Construct the inscribed and
circumscribed circles of a triangle,
and prove properties of angles for a
quadrilateral inscribed in a circle.
G-C 2: Identify and describe
relationships among inscribed
angles, radii, and chords. Include
the relationship between central,
inscribed, and circumscribed
angles; inscribed angles on a
diameter are right angles; the radius
of a circle is perpendicular to the
tangent where the radius intersects
the circle.
-find angle and arc
measures with tangent
lines and chords
-find angle and arc
measures with angles
inside and outside
circles
R: Geometry textbook
chapter 10.5
L: Find arc measures with tangent
lines.
M: Find one angle measure using
inside or outside measurements.
H: Find several angle measures using
inside or outside measurements.
G-C 2: Identify and describe
relationships among inscribed
angles, radii, and chords. Include
the relationship between central,
inscribed, and circumscribed
angles; inscribed angles on a
diameter are right angles; the radius
of a circle is perpendicular to the
tangent where the radius intersects
the circle.
-segments of the chord
theorem
-find lengths of
segments inside a circle
-segments of secants
theorem
-find lengths of
segments from secants
-segments of secants
and tangents theorem
-find lengths of chords
from secants and
tangents
R: Geometry textbook
chapter 10.6
L: Determine segment lengths given
basic numbers.
M: Determine segment lengths given
equations.
H: Determine segment lengths given
complicated equations and word
problems.
G-GPE 1: Derive the equation of a -standard form for the R: Geometry textbook L: Identify the center and radius of a
Geometry Curriculum Guide Page 34
circle of given center and radius
using the Pythagorean Theorem;
complete the square to find the
center and radius of a circle given
by and equation.
G-GPE 4: Use coordinates to prove
simple geometric theorems
algebraically. For example, prove or
disprove that a figure defined by
four given points in the coordinate
plane is a rectangle; prove or
disprove that the point (1, √3) lies
on the circle centered at the origin
and containing the point (0, 2).
equation of a circle,
comes from
Pythagorean Theorem
-write the equation of a
circle given the graph
-write the equation of a
circle given the center
and radius
-graph a circle given the
equation
-apply graphs of circles
to word problems
chapter 10.7 circle given the equation.
M: Graph a circle given the equation.
Write the equation given the graph.
H: Determine if certain points lie on a
circle.
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Pi Day on Fri, March 11
4th 9
Weeks Unit 11: Measuring Length
and Area
Key Understanding Resources, Materials,
and Activities
Assessment Stem
Ch 11
G-GPE 7: Use coordinates to
compute perimeters of polygons
and areas of triangles and
rectangles, e.g., using the distance
formula
G-MG 2: Apply concepts of density
based on area and volume in
modeling situations (e.g., persons
per square mile, BTUs per cubic
-find areas of squares,
rectangles, triangles,
and parallelograms
-Postulate 26- area
Addition Postulate
-solve for unknown
measures, using a
formula
R: Geometry textbook
chapter 11.1
M: Area Notes sheet
L: Find areas of various polygons.
M/H: Find areas of composite figures.
Geometry Curriculum Guide Page 35
foot)
G-GPE 7: Use coordinates to
compute perimeters of polygons
and areas of triangles and
rectangles, e.g., using the distance
formula
G-MG 2: Apply concepts of density
based on area and volume in
modeling situations (e.g., persons
per square mile, BTUs per cubic
foot)
-height of a trapezoid,
perpendicular height
-area of a trapezoid,
rhombus, kite
R: Geometry textbook
chapter 11.2
L: Find areas of various polygons.
M/H: Find areas of composite figures.
G-SRT 5: Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
-review ratios, review
ratios of perimeters in
similar figures
-ratio of areas of similar
figures
-find and apply ratios
for area
R: Geometry textbook
chapter 11.3
L: Identify the relationship between
ratio of sides, ratio of perimeters, and
ratio of areas.
M: Use ratios to find perimeters and
areas of similar figures.
H: Explain how the ratios of similar
figures relates to dilations.
G-C 5: Derive using similarity the
fact that the length of the arc
intercepted by an angle is
proportional to the radius, and
define the radian measure of the
angle as the constant of
proportionality; derive the formula
for the area of a sector.
-review circumference
of a circle
-use the circumference
formula to find distance
traveled
-define arc length, show
how the formula relates
to circumference
-find arc lengths,
circumference, and
radii
R: Geometry textbook
chapter 11.4
L: Find the circumference of a circle.
M: Understand how arc length relates
to circumference and how area of a
sector relates to area of a circle.
H: Understand how circumference can
be used to find distance traveled.
G-C 5: Derive using similarity the
fact that the length of the arc
intercepted by an angle is
proportional to the radius, and
-review area of a circle
-define sector of a circle
-find areas of sectors
R: Geometry textbook
chapter 11.5
L: Find area of a circle and area of a
sector.
M: Find areas of composite figures.
H: Find areas of shaded regions, in
Geometry Curriculum Guide Page 36
define the radian measure of the
angle as the constant of
proportionality; derive the formula
for the area of a sector.
which multiple areas must be found
and subtracted.
G-GPE 7: Use coordinates to
compute perimeters of polygons
and areas of triangles and
rectangles, e.g., using the distance
formula
-define center of the
polygon, radius of the
polygon, apothem of
the polygon, and central
angle of a regular
polygon
-find angle measures
-find perimeter and area
of a regular polygon
R: Geometry textbook
chapter 11.6
L: Find areas of regular polygons.
M/H: Find areas of composite figures.
*There is no common core standard
for this concept.
-define probability vs
geometric probability
-use lengths to find
probability
-use area to find
probability
R: Geometry textbook
chapter 11.7
A: Bean Toss, pg. 770
L: Define probability and understand
how it is used in the real-world.
M: Use lengths to find geometric
probability.
H: Use area to find geometric
probability.
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4th 9
Weeks Unit 12: Surface Area and
Volume of Solids
Key Understanding Resources, Materials,
and Activities
Assessment Stem
G-GMD 4: Identify the shapes of
two-dimensional cross-sections of
three-dimensional objects, and
identify three-dimensional objects
generated by rotations of two-
dimensional objects
-define and identify
nets
-define polyhedron,
faces, edges, and
vertices
-identify and name
polyhedra
-Euler's Theorem
-convex vs concave
R: Geometry textbook
chapter 12.1
R: Geometry textbook pg.
792
L: Determine if the solid is a
polyhedra or not polyhedra.
M: Name the solid. Name the cross-
section.
H: Sketch the given solid. Sketch
solids with cross-sections.
Geometry Curriculum Guide Page 37
-Platonic solids
-describe the cross
section
*There is no common core standard
for this concept.
-define prism, lateral
faces and lateral edges
-define surface area vs
lateral area
-how nets apply to
surface area
-right vs oblique prisms
-find surface area of
prisms
-define cylinder and
right cylinder
-find surface area of a
cylinder
R: Geometry textbook
chapter 12.2
L: Find surface area of solids.
M: Identify solids formed by nets.
H: Find surface areas of composite
figures.
*There is no common core standard
for this concept.
-define pyramid, vertex,
and regular pyramid
-find lateral area and
surface area of a
pyramid
-define cone, vertex,
right cone, lateral
surface
-find lateral area and
surface area of a cone
R: Geometry textbook
chapter 12.3
L: Find surface area of solids.
M: Identify solids formed by nets.
H: Find surface areas of composite
figures.
G-GMD 1: Give an informal
argument for the formulas for the
circumference of a circle, area of a
circle, volume of a cylinder,
pyramid, and cone. Use dissection
arguments, Cavalieri's principle,
and informal limit arguments.
-define volume
-find volume of a cube
-Postulate 29, Volume
Addition Postulate
-find volume of a prism
and cylinder
-Cavalieri's Principle
-volume of an oblique
R: Geometry textbook
chapter 12.4
A: Pg. 825 #33 would be
a great activity
L: Find volume of solids.
M: Find volume of composite figures.
H: Understand and apply density to
problems.
Geometry Curriculum Guide Page 38
G-GMD 2: Give an informal
argument using Cavalieri's principle
for the formulas for the volume of a
sphere and other solid figures
G-GMD 3: Use volume formulas
for cylinders, pyramids, cones, and
spheres to solve problems.
cylinder
G-GMD 3: Use volume formulas
for cylinders, pyramids, cones, and
spheres to solve problems.
-find volume of a
pyramid and cone
-apply trig to find
volume
-find volume of
composite solids
R: Geometry textbook
chapter 12.5
L: Find volume of solids.
M: Find volume of composite figures.
H: Understand and apply density to
problems.
G-GMD 3: Use volume formulas
for cylinders, pyramids, cones, and
spheres to solve problems.
-define sphere, center,
radius, chord, and
diameter
-find surface area of a
sphere
-great circles
-find volume of a
sphere
R: Geometry textbook
chapter 12.6
L: Find surface area and volume of
spheres.
M/H: Find surface area and volume of
composite figures.
*There is no common core standard
for this concept
-define similar solids
-identify similar solids
-Similar Solids
Theorem
-use scale factor of
similar solids
-find the scale factor
-compare similar solids
R: Geometry textbook
chapter 12.7
L: Determine the scale factor when
comparing two solids.
M/H: Understand how changing
measurements will effect the surface
area and volume of solids.
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Geometry Curriculum Guide Page 39
*There is no common core standard
for this concept.
Activity if time allows
-draw isometric and
orthographic views of
various figures
R: Geometry textbook Pg.
551
M: isometric dot paper
L: compare and contrast orthographic
views and isometric views
M: Draw orthographic and isometric
views of figures.
H: Apply orthographic and isometric
views to finding perimeter, area, and
volume of figures.
*There is no common core standard
for this concept
Activity is time allows
-understand the
concepts learned this
year relate to Euclidean
geometry
-discuss various forms
of non-Euclidean
geometry and its history
and arguments for and
against
M: video: Non-Euclidean
Geometry
L: Understand the concepts learned
are based on Euclid's findings.
M: Name some types of non-
Euclidean geometry and their main
ideas.
H: Explain the significance of Euclid's
findings during the time period and
how this would have affected others,
especially those who did not agree
with him.
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Updated August 2015
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