-Reflect, translate, rotate, & dilate objects -Differentiate between congruence and noncongruence motions -Understand reverse orientation -Conceptualize reflectional & rotational symmetry - Relate polygons & solids -build solids -compare & contrast prisms, pyramids, & polyhedrons -identify translational vs. rotational solids - Measure geometric objects -Use standard units to measure length and angles -Deduce methods for measuring area and volume -Dilate geometric objects -Dilate objects -Understand dilation as a similarity motion -Use measurements within dilated figures - Use angles -Identify supplementary & vertically opposite angles -Define perpendicularity -Understand the relationship of angles created by parallel lines -Apply the rules governing internal & external angles of triangles and other polygons - Know the properties of polygons -Understand the properties of circles, triangles, & quadrilaterals -Identify properties unique to regular polygons -Define & measure circumference - Apply coordinates to geometric problems -Use coordinates to place, locate, and move objects -Measure, identify & compare slope -Measure distance using coordinates - Work with proofs using parallel lines - Prove lines to be parallel, -Use properties of parallel lines in proofs -Identify and work with off-scale drawings - Calculate area & perimeter -Discover the formulas for calculating the areas of: triangles, quadrilaterals, other polygons, and circles -Apply the pythagorean theorem -Compare the areas of similar polygons - Identify and prove triangle similarity & congruence -Define similar & congruent triangles -Apply similarity & congruence theorems: AAA, SSS, SAS, ASA, -Understand the properties of special right triangles (45-45-90) -Tangent ratio -Apply knowledge of proportions in right triangles - Calculate volume & surface area -Deduce & apply formulas for calculating the volume of solids, including: prisms, pyramids, cylinders, cones, & spheres -Identify & compare similar solids -Calculate the surface areas of cones & spheres - Create proofs about polygons -Apply logic & accumulated geometric knowledge to the writing of proofs about quadrilaterals & triangles - Understand the structures & properties of circles -Find the measure of arcs -Define, identify & create tangent lines -Use arcs to find inscribed angles -Create proofs using circles - Other Coordinate Systems -Conceptualize coordinates in 3 dimensional space 57