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CPM Geometry Textbook to Curriculum Map Alignment for CC Geometry
High School Geometry – Unit 1
Develop the ideas of congruence through constructions and transformations
Critical Area: In this Unit the notion of two-dimensional shapes as part of a generic plane (the Euclidean Plane) and exploration of transformations of this plane
as a way to determine whether two shapes are congruent or similar are formalized. Students use transformations to prove geometric theorems. The definition of
congruence in terms of rigid motions provides a broad understanding of this notion, and students explore the consequences of this definition in terms of
congruence criteria and proofs of geometric theorems. Students develop the ideas of congruence and similarity through transformations.
CLUSTERS COMMON CORE STATE CPM Geometry Resources
STANDARDS
Make geometric construction Geometry - Congruence 3.1.1, 5.2.1, 6.2.5, 7.1.1,7.1.2, 7.1.4, Materials:
Make a variety of formal geometric G.CO.12 Make formal geometric 7.2.1,7.2.2,8.1.1, 9.2.1- 9.2.4, 10.1.1- For Students: compass, protractor,
constructions using a variety of tools. constructions with a variety of tools 10.1.5, 11.1.1-11.1.3 straight-edge, string, reflective
and methods (compass and devices, tracing paper, graph paper
straightedge, string, reflective devices, MN: 9.2.3 and geometric software.
paper folding, dynamic geometric
software etc. Copying a segment, 9-98, 9-104, 9-110, 9-113, 10-8 For instruction: Document camera,
copying an angle; bisecting a LCD projector, screen
segment; bisecting an angle;
constructing perpendicular lines
including the perpendicular bisector of Tulare County Office of
a line segment; and constructing a line Education
parallel to a give line through a point Hands-On Strategies for
not on the line. Transformational Geometry
G.CO.13 Construct an equilateral 9.2.1, 9.2.3, 9.2.4 Websites:
triangle, a square, a regular hexagon 9-67, 9-104 Math Open Reference
inscribed in a circle. http://mathopenref.com/tocs/constructi
onstoc.html
(online resource that illustrates how to
generate constructions)
Math is Fun
http://www.mathsisfun.com/geometry/
constructions.html H-G.CO.12, 13
Engage New York
Geometry-Module 1 pg 7 – 37
Illustrative Mathematics
LAUSD Secondary Mathematics April 20, 2015 Draft Page 1
CPM Geometry Textbook to Curriculum Map Alignment for CC Geometry
CLUSTERS COMMON CORE STATE CPM Geometry Resources
STANDARDS
Make Formal Constructions
More Constructions
Experiment with transformations in Geometry - Congruence Interactive
the plan G.CO.1 Know precise definitions of MN: 1.1.5, 1.2.5, 2.1.1, 2.1.2, 7.1.2, http://www.shodor.org/interactivate/act
angle, circle, perpendicular lines, 7.1.4, 8.3.2, 10.1.1, 10.1.2 ivities/Transmographer/
Develop precise definitions of parallel lines, and line segment, based
geometric figures based on the on the undefined notions of point, line, Illustrative Mathematics
undefined notions of point, line, distance along a line, and distance Fixed Points of rigid Motion
distance along a line and distance around a circular arc. Dilations and Distances
around a circular arc. Horizontal Stretch of Plane
G.CO.2 Represent transformations in 1.2.1–1.2.6, 3.1.1–3.1.3, 6.2.5
the plane using e.g. transparencies 1-96, 1-102, 2-33, 3-17, 3-42, 5-90, Mars Tasks:
Experiment with transformations in and geometry software; describe 6-28, 9-23 Aaron’s Designs
the plane. transformations as functions that take Possible Triangle Constructions
points in the plane as inputs and give Transforming 2D Figures
other points as outputs. Compare
transformations that preserve distance Mathematics Vision Project:
and angle to those that do not (e.g. Module 6: Congruence, Constructions
translation versus horizontal stretch.) and Proof
1.2.4–1.2.6
G.CO.3 Given a rectangle, 1-64, 2-129, 6-16, 6-65 Module 5: Geometric Figures
parallelogram, trapezoid, or regular
polygon, describe the rotations and Illuminations
reflections that carry it onto itself.
Security Camera Placement
G.CO.4 Develop definitions of 1.2.1–1.2.6 Placing a Fire Hydrant
rotations, reflections, and translations MN: 1.1.1, 1.2.2, 1.2.4 Pizza Delivery Regions
in terms of angles, circles For applications in homework, see Perplexing Parallelograms
perpendicular lines, parallel lines, and standard G-CO.5.
line segments.
California Mathematics
G.CO.5 Given a geometric figure and 1.2.1–1.2.6, 6.2.5 Project
a rotation, reflection or translation, 1-85, 1-126, 2-20, 2-22, 2-64, 3-5, Transformational Geometry
draw the transformed figure using e.g. 3-69, 3-28, 6-52, 7-17
graph paper, tracing paper, or Teaching Channel
geometry software. Specify a Collaborative Work with
sequence of transformations that will Transformations
carry a given figure onto another.
LAUSD Secondary Mathematics April 20, 2015 Draft Page 2
CPM Geometry Textbook to Curriculum Map Alignment for CC Geometry
CLUSTERS COMMON CORE STATE CPM Geometry Resources
STANDARDS
Understand congruence in terms of Geometry - Congruence Reflect on Background Knowledge Illustrative Mathematics
rigid motions 5.1 Angles of Triangles Understand Congruence in terms of
G.CO.6 Use geometric descriptions of Rigid Motion
Use rigid motion to map rigid motions to transform figures and 1.2.1–1.2.6, 3-73, 6.1.1–6.1.3, 6.2.5
corresponding parts of congruent to predict the effect of a given rigid 3-69, 3-76, 6-17, 6-26, 6-65. Is this a rectangle?
triangle onto each other. motion on a given figure; given two For applications of rigid motions in
figures, use the definition of homework, see standard G-CO.5. Illuminations
Explain triangle congruence in terms congruence in terms of rigid motions
of rigid motions. to decide if they are congruent. Triangle Classification
G.CO.7 Use definition of congruence
in terms of rigid motions to show that 6.1.1–6.1.3 Teaching Channel
two triangles are congruent if and only MN: 3.2.2 Formative Assessment: Understanding
if corresponding pairs of sides and Congruence
corresponding pairs of angles are For applications in homework, see
congruent. standard G-SRT.5.
G.CO.8 Explain how the criteria for
triangle congruence (ASA, SAS, and
SSS) follow the definition of 6.1.1–6.1.3
congruence in terms of rigid motions. MN: 6.1.4
For applications in homework, see
standard G-SRT.5.
Prove geometric theorems Geometry - Congruence Illustrative Mathematics
Prove theorems about lines and angles, G.CO.9 Prove theorems about lines 2.1.1–2.1.5, 9.2.1, 6.1.5 https://www.illustrativemathematics.or
triangles; and parallelograms. and angles. Theorems include: vertical MN: 2.1.4, 2.1.5 g/content-standards/HSG/CO/B
angles are congruent; when a Checkpoint 8
transversal crosses parallel lines, 2-33, 6-62, 6-94, 7-67, 7-113, Mars Task:
alternate interior angles are congruent 7-124 Evaluating Statements About
and corresponding angles are Length and Area
congruent; points on a perpendicular
bisector of a line segment are exactly Illuminations:
those equidistant from the segment’s
LAUSD Secondary Mathematics endpoints. April 20, 2015 Draft Page 3
CPM Geometry Textbook to Curriculum Map Alignment for CC Geometry
CLUSTERS COMMON CORE STATE CPM Geometry Resources
STANDARDS
1-84, 2.1.4, 2.1.5, 5.2.1, 6.1.4, Perplexing Parallelograms
G.CO.10 Prove theorems about 6.1.5, 7.2.6, 9.2.4
triangles. Theorems include: MN: 2.2.1, 5.3.1, 7.2.6, 9.2.4
measures of interior angles of a Checkpoint 8
triangle sum to 180°; base angles of 2-20, 4-70, 6-46, 7-69, 7-134, 8-8,
isosceles triangles are congruent; the 8-30, 8-134, 9-33, 12-53
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.
G.CO.11 Prove theorems about
parallelograms. Theorems include: 7.2.1–7.2.6
opposite sides are congruent, opposite MN: 7.2.3, 7.2.4, 8.1.2, 9.2.2
angles are congruent; the diagonals of 7-32, 7-35, 7-100, 7-108, 7-113,
a parallelogram bisect each other, and 7-124, 7-155, 8-87
conversely, rectangles are
parallelograms with congruent
diagonals.
LAUSD Secondary Mathematics April 20, 2015 Draft Page 4
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