CCSS.Math.Content.HSG-CO.A Experiment with transformations in the plane
CCSS.Math.Content.HSG-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.
CCSS.Math.Content.HSG-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).
CCSS.Math.Content.HSG-CO.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.
CCSS.Math.Content.HSG-CO.B Understand congruence in terms of rigid motions
CCSS.Math.Content.HSG-CO.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.
CCSS.Math.Content.HSG-CO.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.
CCSS.Math.Content.HSG-CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
CCSS.Math.Content.HSG-CO.D Make geometric constructions
CCSS.Math.Content.HSG-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
CCSS.Math.Content.HSG-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
CCSS.Math.Content.HSG-C.B Find arc lengths and areas of sectors of circles
CCSS.Math.Content.HSG-C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
CCSS.Math.Content.HSG-GPE Expressing Geometric Properties with Equations
CCSS.Math.Content.HSG-GPE.A Translate between the geometric description and the equation for a conic section
CCSS.Math.Content.HSG-GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
CCSS.Math.Content.HSG-GPE.B Use coordinates to prove simple geometric theorems algebraically
CCSS.Math.Content.HSG-GPE.4 Use coordinates to prove simple geometric theorems algebraically.
CCSS.Math.Content.HSG-GPE.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).
CCSS.Math.Content.HSG-GMD.B Visualize relationships between two-dimensional and three-dimensional objects
CCSS.Math.Content.HSG-GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
CCSS.Math.Content.HSG-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).