2.1 Develop mathematical arguments about geometric relationships

2.1.1 Understand and identify undefined terms: point, line, plane

2.1.2 Investigate postulates about points, lines, and planes

2.1.3 Define and make geometry conjectures

2.1.4 Identify patterns and use inductive reasoning

2.1.5 Understand the meaning of the term proof

2.1.6 Use conditionals in logical arguments

2.1.7 Form converses of conditionals

2.1.8 Use principles of logic to create definitions

2.1.9 Identify and use Algebraic properties of equality

2.1.10 Link the steps of a proof using properties and postulates

2.1.11 Develop theorems from conjectures

2.1.12 Write two-column and paragraph proofs

2.1.13 Make conjectures and prove theorems using postulates and properties of parallel lines and transversals

2.1.14 Develop, identify, and use congruence postulates and theorems for triangles

2.1.15 Develop and use similarity tests for triangles

2.2 Analyze characteristics and properties of two- and three-dimensional geometric shapes

2.2.1 Name and identify parts of an angle

2.2.2 Identify and use special pairs of angles

2.2.3 Describe relationships among lines, parts of lines, and planes

2.2.4 Identify the properties of quadrilaterals and the relationships among the properties

2.2.5 Identify and name circles, major arcs, minor arcs and semicircles

2.2.6 Identify segments, lines and angles related to circles

2.2.7 Identify relationship between arcs and chords

2.2.8 Identify segments and lines related to spheres

2.2.9 Describe properties of geometric figures, such as closed, convex, etc.

2.2.10 Identify and name polygons

2.2.11 Name types of prisms, cylinders, pyramids and cones and identify their parts

2.3 Use visualization, spatial reasoning, and geometric modeling to solve problems

2.3.1 Solve problems by using congruent polygons

2.3.2 Use congruence to develop and use congruence of corresponding parts and the Isosceles Triangle Theorem

2.3.3 Develop conjectures about special polygons use ratios and proportions to solve problems

2.3.4 Identify similar shapes

2.3.5 Identify and apply the Pythagorean Theorem and its converse

2.3.6 Identify and use special right triangles

2.3.7 Solve real-world problems involving segments, lines and circles

2.3.8 Find circumference of circles and lengths of arcs

2.3.9 Solve real-world problems involving circumference and arc length

2.3.10 Represent lines and shapes on spheres

2.3.11 Explore geometry on real-world spheres

2.3.12 Explore probabilities using areas

2.3.13 Compare areas of similar figures

2.3.14 Use areas to solve real-world problems

2.3.15 Compare volumes and surface areas of similar solids

2.3.16 Use formulas for volume and surface area to solve real-world problems involving three-dimensional solids

2.4 Specify locations and describe spatial relationships using coordinate geometry and other representational systems

2.4.1 Write equations for circles

2.4.2 Graph circles given an equation

2.4.3 Find the length of a segment using the distance formula

2.4.4 Find coordinates of the midpoint of a segment

2.4.5 Find the slope of a line

2.4.6 Write equations of lines

2.4.7 Compare slopes of parallel and perpendicular lines

2.4.8 Write equations for parallel and perpendicular lines

2.4.9 Place figures on coordinate axes and label vertices

2.4.10 Prove theorems using coordinate geometry

2.5 Apply transformations and use symmetry to analyze mathematical situations

2.5.1 Locate a set of points in a plane or in space given certain conditions

2.5.2 Identify and perform reflections, rotations, translations and dilations

2.5.3 Describe and draw objects having line symmetry and point symmetry

2.5.4 Analyze real-world situations using symmetry

2.5.5 Use coordinate geometry to perform transformations

2.5.6 Represent transformations using matrices

2.5.7 Describe magnitude and directions of vectors

2.5.8 Identify horizontal and vertical components of vectors

2.5.9 Calculate and interpret scalar multiplication of vectors

2.5.10 Calculate and interpret vector sums

2.5.11 Use vectors to analyze real-world situations

2.6 Apply appropriate techniques, tools, and formulas to determine measurements

2.6.1 Measure, draw, and classify angles

2.6.2 Construct figures using compass and straightedge

2.6.3 Develop and use formulas for the sums of the measures of interior and exterior angles of a polygon

2.6.4 Solve problems using the Pythagorean Theorem

2.6.5 Use the tangent, sine, and cosine rations to solve problems

2.6.6 Find the measure of arcs

2.6.7 Find measures of angles and arcs formed by segments intersecting circles

2.6.8 Find lengths of segments formed by chords, tangents and secants

2.6.9 Find the interior and exterior angle sums of polygons

2.6.10 Determine each angle in regular polygons

2.6.11 Use angles and angle sums to solve real-world problems involving polygons

2.6.12 Find the areas of triangles and parallelograms

2.6.13 Find the areas of regular polygons and circles

2.6.14 Find the areas of sectors of circles

2.6.15 Find volumes, lateral areas and surface areas of right prisms, cylinders, cones and regular pyramids

2.6.16 Calculate the surface area and volume of spheres

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