Conceptual Category Geometry

HS.G.1Know and apply precise definitions of the language of Geometry: (MP.3, MP.6)HS.G.10Apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (MP.3, MP.6)HS.G.11Understand theorems about triangles. (MP.1, MP.3)HS.G.12Understand properties of right triangles. (MP.3, MP.4)HS.G.13(+)Derive the formula A=1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. (MP.6, MP.7)HS.G.14(+)Understand and apply the Law of Sines and the Law of Cosines. (MP.1, MP.3)HS.G.15Verify using dilations that all circles are similar. (MP.5, MP.8)HS.G.16Identify and describe relationships among angles and segments within the context of circles involving: (MP.3, MP.5, MP.7)HS.G.17(+)Apply basic construction procedures within the context of a circle. (MP.5, MP.6)HS.G.18(+)Understand the relationship between an intercepted arc length within a circle and the radius of the circle. (MP.2, MP.3)HS.G.19Understand the relationship between the algebraic form and the geometric representation of a circle. (MP.6, MP.8)HS.G.2Representing transformations in the plane. (MP.5, MP.7)HS.G.20(+)Derive the equations of conic sections. (MP.2, MP.7)HS.G.21Use coordinates to justify and prove simple geometric theorems algebraically. (MP.2, MP.6)HS.G.22Justify and apply the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. (MP.3, MP.7)HS.G.23Find measurements among points within the coordinate plane. (MP.2, MP.8)HS.G.24Use coordinates within the coordinate plane to calculate measurements of two dimensional figures. (MP.2, MP.4)HS.G.25Analyze and determine the validity of arguments for the formulas for the various figures and shapes. (MP.3, MP.7)HS.G.26(+)Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. (MP.2, MP.5)HS.G.27Use volume formulas to solve problems for cylinders, pyramids, cones, spheres, prisms. (MP.4, MP.6)HS.G.28Identify the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects. (MP.5, MP.7)HS.G.29Use geometric shapes, their measures and their properties to describe objects in real world settings. (MP.1, MP.4)HS.G.3(+)Develop formal definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments. (MP.6, MP.7)HS.G.30Apply concepts of density based on area and volume in modeling situations, using appropriate units of measurement. (MP.4, MP.6)HS.G.31Apply geometric methods to solve design problems. (MP.1, MP.4)HS.G.4Understand the effects of transformations of geometric figures. (MP.2, MP.8)HS.G.5Know and apply the concepts of triangle congruence: (MP.3, MP.6)HS.G.6Apply theorems for lines, angles, triangles, parallelograms. (MP.2, MP.3)HS.G.7Prove theorems about geometric figures. (MP.6, MP.7)HS.G.8Create and apply geometric constructions. (MP.5, MP.6)HS.G.9Understand properties of dilations. (MP.5, MP.7)
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