Unit 1: 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. Unit 1: Congruence, Proof, and Constructions Cluster Standard Practices Cluster Note: Build on student experience with rigid Make sense of motions from earlier grades. Point out the basis of rigid problems and motions in geometric concepts, e.g., translations move persevere in solving points a specified distance along a line parallel to a specified them. line; rotations move objects along a circular arc with a specified center through a specified angle. Reason abstractly and G.CO.1 Know precise definitions of angle, circle, perpendicular quantitatively. line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around Construct viable a circular arc. arguments and critique the Experiment with Essential Skills and Knowledge reasoning of others. transformations in Ability to fluently use mathematical vocabulary the plane. Model with mathematics. G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe Use appropriate transformations as functions that take points in the plane as tools inputs and give other points as outputs. Compare strategically. transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch) Attend to precision. Essential Skills and Knowledge Look for and make Ability to make connections between function transformations (F.BF.3) and geometric use of structure. transformations Knowledge that rigid transformations preserve the Look for and express shape of a figure regularity in repeated reasoning.
Unit 1: 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. Unit 1: Congruence, Proof, and Constructions Cluster Standard Practices Experiment with transformations in the plane. Cluster Note: 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.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. Essential Skills and Knowledge Ability to fluently use mathematical vocabulary 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) Essential Skills and Knowledge Ability to make connections between function transformations (F.BF.3) and geometric transformations Knowledge that rigid transformations preserve the shape of a figure Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
GeometryFramework.docx