HSG.CO.A.2 Represent transformations in the plane (e.g. using transparencies, tracing paper, geometry software, etc.). 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 dilation).
HSG.CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure, (e.g., using graph paper, tracing paper, miras, geometry software, etc.). Specify a sequence of transformations that will carry a given figure onto another.
HSG.CO.2 Understand congruence in terms of rigid motions
HSG.CO.B.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.
HSG.CO.B.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.
HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Investigate congruence in terms of rigid motion to develop the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL).
HSG.CO.E.14 Apply inductive reasoning and deductive reasoning for making predictions based on real world situations using: Conditional Statements (inverse, converse, and contrapositive); Venn Diagrams.
HSG.SRT Similarity, Right Triangles, and Trigonometry
HSG.SRT.6 Understand similarity in terms of similarity transformations
HSG.SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
HSG.SRT.A.2 Given two figures: Use the definition of similarity in terms of similarity transformations to determine 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.
HSG.SRT.B.5 Use congruence (SSS, SAS, ASA, AAS, and HL) and similarity (AA~, SSS~, SAS~) criteria for triangles to solve problems. Use congruence and similarity criteria to prove relationships in geometric figures.
HSG.C.11 Find arc lengths and areas of sectors of circles
HSG.C.B.5 Derive using similarity that the length of the arc intercepted by an angle is proportional to the radius. Derive and use the formula for the area of a sector. Understand the radian measure of the angle as a unit of measure.
HSG.MG.A.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).