Unit 3 Geometry Concepts & Connections PDF

Geometry Concepts & Connections -- Unit 3 Exploring Congruence Main Standard: 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...

Geometry Concepts & Connections -- Unit 3 Exploring Congruence Main Standard: 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. Standards/Learning Objectives Learning Goals Select Vocabulary G.GSR.3.1 Use geometric reasoning and Students should be able to define and identify Transformation symmetries of regular polygons to develop figures as preimages and images. Translation definitions of rotations, reflections, and Reflection translations. Students should be provided with multiple Line of Reflection opportunities to identify lines of symmetry and Rotation (Clockwise & CCW) angles of rotation to map a figure onto itself. Line symmetry Rotational symmetry Students should be provided with multiple Preimage opportunities to identify angles of rotation, lines Image of reflection, and directions of translations to map a preimage onto its image. Students should be provided opportunities to experiment with transformations represented on and off the coordinate plane G.GSR.3.2 Verify experimentally the Students should be able to determine that Rigid Motions (Rigid Transformations) congruence properties of rotations, translations, reflections, and rotations produce Congruence reflections, and translations: lines are images of the same size and shape as the Congruence Statements taken to lines and line segments to line preimage. segments of the same length; angles are Students should be able to determine taken to angles of the same measure; congruency by identifying the rigid parallel lines are taken to parallel lines. transformation(s) that produced the image of a figure.  Opportunities should be provided for students to write statements of congruency. Students should have ample opportunities to use geometric tools and/or technology to explore figures created from translations, reflections, and rotations. G.GSR.3.3 Use geometric descriptions of Students should be given multiple opportunities Corresponding Parts (Sides & Angles) rigid motions to draw the transformed to identify resulting coordinates from figures and to predict the effect on a given translations, reflections, and rotations, and figure. Describe a sequence of recognize the relationship between the transformations from one figure to coordinates and the transformation. another and use transformation properties to determine congruence. Given two figures, students should be able to use the definition of congruence in terms of rigid motions to verify congruence if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Students should be able to use function notation to represent transformations in the coordinate plane. G.GSR.3.4 Explain how the criteria for Students should be able to apply properties of Logic triangle congruence follow from the congruence to solve problems with missing Conditional Statement definition of congruence in terms of rigid values involving corresponding parts. Inverse Statement motions. Use congruency criteria for Contrapositive statements triangles to solve problems and to prove Students should be able to use the definition of Two-column proof relationships in geometric figures. congruence to prove relationships in geometric Flow proof figures. SSS theorems  SAS theorems Students should be provided opportunities to ASA theorems use ASA, SAS, SSS, AAS, and HL congruence AAS theorems postulates/theorems to prove triangles are HL theorems congruent. Students should have opportunities to prove triangle congruence using appropriate methods: logic statements, two-column proofs, paragraph proofs, and flow proofs.