Download geometry - Sisseton School District 54-2

UNIT 1
GEOMETRY
TEMPLATE CREATED BY
REGION 1 ESA
UNIT 1
Geometry Math Tool Unit 1
Traditional Pathway: Geometry
The fundamental purpose of the course in Geometry is to formalize and extend students’ geometric experiences from the middle grades. Students
explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical
arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example,
transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual
category found in the high school CCSS. The Mathematical Practice Standards apply throughout each course and, together with the content
standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense
of problem situations. The critical areas, organized into six units are as follows.
Critical Area 1: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid
motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In
this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence
as a familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about
triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
Critical Area 2: Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They
identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle
trigonometry, with particular attention to special right triangles and the Pythagorean theorem. Students develop the Laws of Sines and Cosines in
order to find missing measures of general (not necessarily right) triangles, building on students’ work with quadratic equations done in the first
course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles.
Critical Area 3: Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of
circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of crosssections and the result of rotating a two-dimensional object about a line.
Critical Area 4: Building on their work with the Pythagorean theorem in 8th grade to find distances, students use a rectangular coordinate system
to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which
relates back to work done in the first course. Students continue their study of quadratics by connecting the geometric and algebraic definitions of
the parabola.
Template created by Region 1 ESA
Page 2 of 16
Geometry Math Tool Unit 1
Critical Area 5: In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem,
and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on
chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the
equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate
plane, and apply techniques for solving quadratic equations, which relates back to work done in the first course, to determine intersections
between lines and circles or parabolas and between two circles.
Critical Area 6: Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to
compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent
events, and conditional probability. Students should make use of geometric probability models wherever possible. They use probability to make
informed decisions.
Note:
It is important to note that the units (or critical areas) are intended to convey coherent groupings of content. The clusters and standards within units are ordered
as they are in the Common Core State Standards, and are not intended to convey an instructional order. Considerations regarding constraints, extensions, and
connections are found in the instructional notes. The instructional notes are a critical attribute of the courses and should not be overlooked. For example, one
will see that standards such as A.CED.1 and A.CED.2 are repeated in multiple courses, yet their emphases change from one course to the next. These changes are
seen only in the instructional notes, making the notes an indispensable component of the pathways.
(All instructional notes/suggestions will be found in italics throughout this document)
★- Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol
Geometry Unit 1 Overview: Congruence, Proof, and Constructions
In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions:
translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit,
students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a
familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about
triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
Template created by Region 1 ESA
Page 3 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions- G.CO.1
Cluster: Experiment with transformations in the plane.
Standard
Instructional Notes: Build on student experience with rigid
motions from earlier grades. Point out the basis of rigid
motions in geometric concepts, e.g., translations move points a
specified distance along a line parallel to a specified line;
rotations move objects along a circular arc with a specified
center through a specified angle.

I can indentify undefined notions used in
geometry (point, line, plane, distance) and
describe their characteristics.

I can identify angles, circles, perpendicular
lines, parallel lines, rays, and line segments.
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.

I can define angles, circles, perpendicular
lines, parallel lines, rays, and line segments
precisely using the undefined terms and “ifthen” and “if-and-only-if” statements.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Undefined terms, point, line, plane, distance, angle, circle, perpendicular, parallel, line segment,
arc, ray, vertex, equidistant, intersect, right angle
Page 4 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions- G.CO.2
Cluster: Experiment with transformations in the plane.
Standard
Instructional Notes: Build on student experience with rigid
motions from earlier grades. Point out the basis of rigid
motions in geometric concepts, e.g., translations move points a
specified distance along a line parallel to a specified line;
rotations move objects along a circular arc with a specified
center through a specified angle.
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).








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can draw transformations of reflections,
rotations, translations, and combinations of
these using graph paper, transparencies,
and/or geometry software.

I can determine the coordinates for the
image (output) of a figure when a
transformation rule is applied to the preimage (input).

I can distinguish between transformations
that are rigid (preserve distance and angle
measure-reflections, rotations, translations,
or combinations of these) and those that are
not (dilations or rigid motions followed by
dilations).
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Transformation, reflection, rotation, translation, dilation, image, pre-image, rigid motion, input,
output, coordinates, distance, angle measure
Page 5 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions- G.CO.3
Cluster: Experiment with transformations in the plane.
Standard
Instructional Notes: Build on student experience with rigid
motions from earlier grades. Point out the basis of rigid
motions in geometric concepts, e.g., translations move points a
specified distance along a line parallel to a specified line;
rotations move objects along a circular arc with a specified
center through a specified angle.
G.CO.3 Given a rectangle, parallelogram, trapezoid, or
regular polygon, describe the rotations and reflections that
carry it onto itself.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can describe and illustrate how a
rectangle is mapped onto itself using
transformations.

I can describe and illustrate how a
parallelogram is mapped onto itself using
transformations.

I can describe and illustrate how an
isosceles trapezoid is mapped onto itself
using transformations.

I can calculate the number of lines of
reflection symmetry and the degree of
rotational symmetry of any regular
polygon.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Rectangle, parallelogram, trapezoid, isosceles trapezoid, regular polygon, rotational symmetry,
reflection symmetry, mapped onto
Page 6 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions- G.CO.4
Cluster: Experiment with transformations in the plane.
Standard
Instructional Notes: Build on student experience with rigid
motions from earlier grades. Point out the basis of rigid
motions in geometric concepts, e.g., translations move points a
specified distance along a line parallel to a specified line;
rotations move objects along a circular arc with a specified
center through a specified angle.


G.CO.4 Develop definitions of rotations, reflections, and
translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.









Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can construct the reflection definition by
connecting any point on the pre-image to its
corresponding point on the reflected image and
describing the line segment’s relationship to the
line of reflection (i.e., the line of reflection is the
perpendicular bisector of the segment.
I can construct the translation definition by
connecting any point on the pre-image to its
corresponding point on the translated image and
connecting a second point on the pre-image to
its corresponding point on the translated image,
and describing how the two segments are equal
in length, point in the same direction, and are
parallel.
I can construct the rotation definition by
connecting the center of rotation to any point on
the pre-image and to its corresponding point on
the rotated image, and describing the measure of
the angle formed and the equal measures of the
segments that formed the angle as part of the
definition.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Rotation, reflection, translation, perpendicular bisector, line segment, pre-image, image, parallel
lines, angle, center of rotation
Page 7 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions- G.CO.5
Cluster: Experiment with transformations in the plane.
Standard
Instructional Notes: Build on student experience with rigid
motions from earlier grades. Point out the basis of rigid
motions in geometric concepts, e.g., translations move points a
specified distance along a line parallel to a specified line;
rotations move objects along a circular arc with a specified
center through a specified angle.
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can draw a specific transformation when
given a geometric figure and a rotation,
reflection, or translation.

I can predict and verify the sequence of
transformations (a composition) that will
map a figure onto another.
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.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Refection, rotation, translation, figure, map, transformation, composition
Page 8 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions- G.CO.6
Cluster: Understand congruence in terms of rigid motions.
Standard
Instructional Notes: Rigid motions are at the foundation of the
definition of congruence. Students reason from the basic
properties of rigid motions (that they preserve distance and
angle), which are assumed without proof. Rigid motions and
their assumed properties can be used to establish the usual
triangle congruence
criteria, which can then be used to prove other theorems.
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.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can define rigid motions as reflections,
rotations, translations, and combinations of
these, all of which preserve distance and
angle measure.

I can define congruent figures as figures that
have the same shape and size and state that
a composition of rigid motions will map one
congruent figure onto another.

I can predict the composition of
transformations that will map a figure onto a
congruent figure.

I can determine if two figures are congruent
by determining if rigid motions will turn one
figure into the other.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Congruence, composition, rigid motions, map, reflections, rotation, translation, transformation,
angle measure, distance
Page 9 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.7
Cluster: Understand congruence in terms of rigid motions.
Standard
Instructional Notes: Rigid motions are at the foundation of the
definition of congruence. Students reason from the basic
properties of rigid motions (that they preserve distance and
angle), which are assumed without proof. Rigid motions and
their assumed properties can be used to establish the usual
triangle congruence criteria, which can then be used to prove
other theorems.
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.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can identify corresponding sides and
corresponding angles of congruent triangles.

I can explain that in a pair of congruent
triangles, corresponding sides are congruent
(distance is preserved) and corresponding
angles are congruent (angle measure is
preserved).

I can demonstrate that when distance is
preserved (corresponding sides are
congruent) and angle measure is preserved
(corresponding angles are congruent) the
triangles must also be congruent.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Rigid motions, reflection, rotation, translation, distance, angle measure, congruent, composition,
map, figure, corresponding sides, corresponding angles, triangle
Page 10 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.8
Cluster: Understand congruence in terms of rigid motions.
Standard
Instructional Notes: Rigid motions are at the foundation of the
definition of congruence. Students reason from the basic
properties of rigid motions (that they preserve distance and
angle), which are assumed without proof. Rigid motions and
their assumed properties can be used to establish the usual
triangle congruence criteria, which can then be used to prove
other theorems.

I can define rigid motions as reflections,
rotations, translations, and combinations of
these, all of which preserve distance and
angle measure.

I can list the sufficient conditions to prove
triangles 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.

I can map a triangle with one of the
sufficient conditions (e.g., SSS) onto the
original triangle and show that
corresponding sides and corresponding
angles are congruent.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Rigid motion, reflection, rotation, translation, congruent, composition, map, SSS, SAS, ASA
Page 11 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.9
Cluster: Prove geometric theorems.
Standard
Instructional Notes: Encourage multiple ways of writing proofs,
such as in narrative paragraphs, using flow diagrams, in twocolumn format, and using diagrams without words. Students
should be encouraged to focus on the validity of the underlying
reasoning while exploring a variety of formats for expressing
that reasoning.
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.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets

I can identify and use the properties of
congruence and equality (reflexive,
symmetric, transitive) in my proofs.
 I can order statements based on the Law of
Syllogism when constructing my proof.
 I can correctly interpret geometric diagrams
by identifying what can and cannot be
assumed.
 I can use the theorems, postulates, or
definitions to prove theorems about lines
and angles, including: a) vertical angles are
congruent, b) when a transversal crosses
parallel lines, alternate interior angles are
congruent and corresponding angles are
congruent, and same-side interior angles are
supplementary, c) points on a perpendicular
bisector of a line segment are exactly those
equidistant from the segment’s endpoints.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Theorem, linear pair, vertical angles, alternate interior angles, alternate exterior, same-side
interior angles, corresponding angles, perpendicular bisector, supplementary angles,
complimentary angles, equidistant, congruent, adjacent, consecutive/non-consecutive, reflection,
Law of Syllogism
Page 12 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.9
Cluster: Prove geometric theorems.
Standard
Instructional Notes: Encourage multiple ways of writing proofs,
such as in narrative paragraphs, using flow diagrams, in twocolumn format, and using diagrams without words. Students
should be encouraged to focus on the validity of the underlying
reasoning while exploring a variety of formats for expressing
that reasoning. Implementation of G.CO.10 may be extended
to include concurrence of perpendicular bisectors and angle
bisectors as preparation for G.C.3 in Unit 5
.
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.
Standards of Mathematical Practice (SMP’s)
 #1 Make sense of problems and persevere in solving
them.
 #2 Reason abstractly and quantitatively.
 #3 Construct viable arguments and critique the reasoning
of others.
 #4 Model with mathematics
 #5 Use appropriate tools strategically.
 #6 Attend to precision.
 #7 Look for and make use of structure
 #8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Target

I can order statements based on the Law of
Syllogism when constructing my proof.

O can correctly interpret geometric diagrams
(what can and cannot be assumed).

I can use theorems, postulates, or definitions
to prove theorems about triangles,
including: a) measures of interior angles of a
triangle sum to 180⁰, b) base angles of
isosceles triangles are congruent, c) the
segment joining midpoints of two sides of a
triangle is parallel to the third side and half
the length, d) the medians of a triangle meet
at a point.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Midpoint, mid-segment isosceles triangle, median, centroid, coordinate proof, adjacent,
consecutive/non-consecutive, Law of Syllogism
Page 13 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.11
Cluster: Prove geometric theorems.
Standard
Suggested Learning Targets
Instructional Notes: Encourage multiple ways of writing proofs,
such as in narrative paragraphs, using flow diagrams, in twocolumn format, and using diagrams without words. Students
should be encouraged to focus on the validity of the underlying
reasoning while exploring a variety of formats for expressing
that reasoning
I can use theorems, postulates, or definitions to
prove theorems about parallelograms, including:
 Prove opposite sides of a parallelogram are
congruent
 Prove opposite angles of a parallelogram are
congruent
 Prove the diagonals of a parallelogram bisect
each other
 Prove that rectangles are parallelograms
with congruent diagonals.
G.CO.11 Prove theorems about parallelograms. Theorems
include: opposite sides are congruent, opposite angles are
congruent, the diagonals of a parallelogram bisect each
other, and conversely, rectangles are parallelograms with
congruent diagonals.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Quadrilateral, parallelogram, rectangle, diagonals, distance formula, midpoint formula, slope,
bisector, congruence properties
Page 14 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.12
Cluster: Make geometric constructions.
Standard
Instructional Notes: Build on prior student experience with
simple constructions. Emphasize the ability to formalize and
explain how these constructions result in the desired objects.
Some of these constructions are closely related to previous
standards and can be introduced in conjunction with them.
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.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets and Type

I can identify the tools used in formal
constructions.

I can use tools and methods to precisely
copy a segment, copy an angle, bisect a
segment, bisect and angle, construct
perpendicular lines and bisectors, and
construct a line parallel to a give line
through a point not on the line.

I can informally perform the constructions
listed above using string, reflective devices,
paper folding, and/or dynamic geometric
software.
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Segment, angle, perpendicular lines, perpendicular bisector, parallel lines, bisect, formal
construction, informal construction, compass, straightedge
Page 15 of 16
Geometry Math Tool Unit 1
Unit 1: Congruence, Proof, and Constructions G.CO.13
Cluster: Make geometric constructions.
Standard
Instructional Notes: Build on prior student experience with
simple constructions. Emphasize the ability to formalize and
explain how these constructions result in the desired objects.
Some of these constructions are closely related to previous
standards and can be introduced in conjunction with them.

I can define inscribed polygons (the vertices
of the figure must be points on the circle.

I can construct an equilateral triangle
inscribed in a circle.
G.CO.13 Construct an equilateral triangle, a square, and a
regular hexagon inscribed in a circle.

I can construct a square inscribed in a circle.

I can construct a hexagon inscribed in a
circle.

I can explain the steps to construction an
equilateral triangle, a square, and a regular
hexagon inscribed in a circle.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving
them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets and Type
Essential Questions/ Enduring Understandings
 In what ways can congruence be useful?
Proving and applying congruence provides a
basis for modeling situations geometrically.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Construction, equilateral triangle, square, regular hexagon inscribe, circle
Page 16 of 16