1 1st Nine Weeks Topic I - Transformations and Congruence 912.G-CO.1: Experiment with transformations in the plane 912.G-CO.1: Experiment with transformations in the plane 912.G-CO.1.1: 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. 912.G-CO.1.1: 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. 912.G-CO.1.2: 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). 912.G-CO.1.2: 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). 912.G-CO.1.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 912.G-CO.1.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 912.G-CO.1.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 912.G-CO.1.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 912.G-CO.1.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Graph an image Sequences of transformations 912.G-CO.1.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Graph an image Sequences of transformations 912.G-CO.2: Understand congruence in terms of rigid motions 912.G-CO.2: Understand congruence in terms of rigid motions 912.G-CO.2.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. 912.G-CO.2.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. 912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. 912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Topic II - Lines, Angles, and Triangles - Part A 912.G-CO.2: Understand congruence in terms of rigid motions 912.G-CO.2: Understand congruence in terms of rigid motions 912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.912.G-CO.2.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions. 912.G-CO.2.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.912.G-CO.2.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions. 912.G-CO.3: Prove geometric theorems 912.G-CO.3: Prove geometric theorems 912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines and angles to solve problems. 912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines and angles to solve problems. 912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. Corresponding parts of congruent triangles Segments and relationships within triangles 912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. Corresponding parts of congruent triangles Segments and relationships within triangles 912.G-CO.4: Make geometric constructions 912.G-CO.4: Make geometric constructions 912.G-CO.4.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Angles Points, lines, and segments Regular polygons Triangles Circles 912.G-CO.4.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Angles Points, lines, and segments Regular polygons Triangles Circles 912.G-CO.4.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. 912.G-CO.4.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. 912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically 912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically 912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).