Module 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 strategically applied a rigid motion to informally show that two triangles are congruent.
       In this module, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They build upon this familiar foundation of triangle congruence to develop formal proof techniques. Students make conjectures and construct viable arguments to prove theorems using a variety of formats and solve problems about triangles, quadrilaterals, and other polygons.
       They construct figures by manipulating appropriate geometric tools (compass, ruler, protractor, etc.)and justify why their written instructions produce the desired figure

Unit 1: Basic Constructions    (G.CO.1, 12, 13)

Students begin this module with Topic A, Constructions.  Major constructions include an equilateral triangle, an angle bisector, and a perpendicular bisector.  Students synthesize their knowledge of geometric terms with the use of new tools and simultaneously practice precise use of language and efficient communication when they write the steps that accompany each construction.

M1.U1 Lessons:

M1.U1.L1
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M1.U1.L2
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M1.U1.L3
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M1.U1.L4
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M1.U1.L5
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Assessments

Reengagement

Unit 2: Unknown Angles         (8.G.5, G.CO.9)

Constructions segue into Topic B, Unknown Angles, which consists of unknown angle problems and proofs.  These exercises consolidate students’ prior body of geometric facts and prime students’ reasoning abilities as they begin to justify each step for a solution to a problem.  Students began the proof writing process in Grade 8 when they developed informal arguments to establish select geometric facts

M1.U2 Lessons:

M1.U2.L6
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M1.U2.L7
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M1.U2.L8
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M1.U2.L9
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M1.U2.L10
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M1.U2.L11
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Assessments
Reengagement

Unit 3: Transformations/Rigid Motions
                                                                                                          (G.CO.2, 3, 4)

Transformations, builds on students’ intuitive understanding developed in Grade 8.  With the help of manipulatives, students observed how reflections, translations, and rotations behave individually and in sequence (8.G.1, 8.G.2).  In Grade 10, this experience is formalized by clear definitions (G.CO.4) and more in-depth exploration (G.CO.3, G.CO.5).  The concrete establishment of rigid motions also allows proofs of facts formerly accepted to be true (G.CO.9).  Similarly, students’ Grade 8 concept of congruence transitions from a hands-on understanding (8.G.2) to a precise, formally notated understanding of congruence (G.CO.6).  With a solid understanding of how transformations form the basis of congruence, students next examine triangle congruence criteria.  Part of this examination includes the use of rigid motions to prove how triangle congruence criteria such as SAS actually work (G.CO.7, G.CO.8).

M1.U3 Lessons:

M1.U3.L12
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M1.U3.L13
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M1.U3.L14
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M1.U3.L15
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M1.U3.L16
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M1.U3.L17
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M1.U3.L18
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M1.U3.L19
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M1.U3.L20
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M1.U3.L21
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Assessments
Reengagement

Unit 4: Congruence                   (G.CO.10, 11)

Proving Properties of Geometric Figures, students use what they have learned in Topics A through C to prove properties—those that have been accepted as true and those that are new—of parallelograms and triangles 

​M1.U4 Lessons:

M1.U4.L22
M1.U4.L23
M1.U4.L25
M1.U4.L26
M1.U4.L27

Unit 5: Proving Properties of Geometric Constructions           (G.CO.9, 10, 11)

This Unit is a review of constructions with some advance properties.

​M1.U5 Lessons:

M1.U5.28
M1.U5.29
M1.U5.30

Unit 6: Proving Properties of Geometric Constructions                (G.CO.13)

This Unit is a review that highlights how geometric assumptions underpin the facts established thereafter.

​M1.U6 Lessons:

M1.U6.L31
M1.U6.L32

Unit 7: Axiomatic Systems            (G.CO.1, 2, 3)

In this unit students review material covered throughout the module.  Additionally, students discuss the structure of geometry as an axiomatic system.

​M1.U7 Lessons:

M1.U7.L33
M1.U7.L34