Geometry Block - Unit 3

Unit 3: Congruence

Geometric & Spatial Reasoning (GSR)

G.GSR.3: Experiment with transformations in the plane to develop precise definitions for translations, rotations, and reflections and use these to describe symmetries and congruence to model and explain real-life phenomena.

STANDARD & Expectations

LT & SC

Lesson Activities & Resources

Days 1 - 3

G.GSR.3.1

Use geometric reasoning and symmetries of regular polygons to develop definitions of rotations, reflections, and translations.

G.GSR.3.2

Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines

G.GSR.3.3

Use geometric descriptions of rigid motions to draw the transformed figures and to predict the effect on a given figure. Describe a sequence of transformations from one figure to another to use transformation properties to determine congruence.

LT: 

• I am learning symmetries to rotate, reflect, and translate regular polygons.

SC:

• I can define and identify figures as preimages and images.

• I can identify lines of symmetry and angles of rotation to map a figure onto itself.

• I can identify angles of rotation, lines of reflection, and directions of translations to map a preimage onto its image.

• I can experiment with transformations represented on and off the coordinate plane. 

LA&R:

• Desmos and 3-Act Tasks; GeoGebra Geometry (free); Transformations booklet & PowerPoint – uses patty paper to discover reflections and rotations; Quizlet vocabulary & word wall.

Days 4

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Quiz over Transformations

Days 5 - 8

G.GSR.3.4

Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions. Use congruence criteria for triangles to solve problems and to prove relationships in geometric figures

LT: 

• I am learning about congruent triangles and CPCTC.

SC:

• I can apply properties of congruence to solve problems with missing values involving corresponding parts.

• I can use the definition of congruence to prove relationships in geometric figures.

• I can use the ASA, SAS, SSS, AAS, and HL congruence theorems and postulates to prove triangles congruent.

• I can write logic statements as conditional, converse, inverse, and contrapositive statements.

• I can prove triangle congruence using logic statements, two-column proofs, paragraph proofs, and flow proofs.

LA&R:

• Desmos and 3-Act Tasks; GeoGebra; Quizlet vocabulary & word wall; notes, practice, and assessments on logic statements & different styles of proofs. Use “Uno” PowerPoint to introduce two-column proofs. Use the “Reasons List” to help familiarize students with possible reasons in proofs; Flipped classroom activity.

Days 9-10

• Test Review

• Test