2.1.2 Study patterns to make a conjecture about a geometric concept.

2.1.3 Recognize when the conditions of a definition have been met.

2.1.4 Recognize the difference between inductive and deductive reasoning and identify the process that is used at a given time.

2.1.5 Use inductive reasoning to make generalizations from an observed pattern.

2.1.6 Determine the truth-value of conditional statements (conditional, converse, inverse, contrapositive, biconditional).

2.1.7 Identify the distinction between a necessary condition and a sufficient condition.

2.1.8 Judge the validity of reasoning that claims to establish proof.

2.1.9 Recognize and explain flaws in invalid arguments.

2.2.2 Use algebraic skills to solve problems involving properties of polygons.

2.2.3 Apply the principles of coordinate geometry to graph lines and recognize geometric properties and relationships.

2.2.4 Apply the principles of coordinate geometry to determine the slope of lines and relate it to parallelism and perpendicularity.

2.2.5 Apply the principles of coordinate geometry to determine the midpoint of a line segment.

2.2.6 Apply the principles of coordinate geometry to determine the length of a line segment.

2.2.7 Apply the principles of coordinate geometry to determine the area of common geometric figures.

2.2.8 Translate between synthetic (Euclidean) and coordinate representations.

2.3.2 Sketch models of, identify, and describe examples of types of lines (intersecting, concurrent, parallel, perpendicular, skew, and congruent line segments).

2.3.3 Demonstrate the meaning of angle, using an appropriate model.

2.3.4 Sketch, identify, and describe types of angles (acute, right, obtuse, straight, complementary, supplementary, adjacent and linear pairs, vertical, and congruent).

2.3.5 Describe, identify, and draw sketches of related postulates.

2.3.6 Through investigation, deduce and apply angle relationships (congruent and supplementary angles) created by parallel lines cut by a transversal.

2.3.7 Use properties of parallel lines cut by a transversal to develop deductive reasoning skills.

2.4.2 Describe, identify, and draw sketches of triangles classified by angle measure.

2.4.3 Demonstrate knowledge of the hierarchy of triangle types and the consequences of it.

2.4.4 Describe and model the relationship between sides, angles, and side-angle measures in a triangle, the triangle inequality, the isosceles base angles theorem, the triangle sum theorem, and properties of mid-segments.

2.4.5 Describe and model the relationship between side and angle measures in two triangles.

2.4.6 Describe, identify, construct, and apply the properties of medians – centroid.

2.4.7 Describe, identify, construct, and apply the properties of altitudes – orthocenter.

2.4.8 Describe, identify, construct, and apply the properties of angle bisectors – incenter.

2.4.9 Describe, identify, construct, and apply the properties of perpendicular bisectors – circumcenter.

2.4.10 Describe, identify, and draw sketches of quadrilaterals (parallelograms, rectangles, squares, rhombuses, trapezoids, and kites.

2.4.11 Through investigation, deduce and apply properties of sides, angles, diagonals, etc.

2.4.12 Demonstrate knowledge of the hierarchy of quadrilateral types and the consequences of it (i.e. Venn Diagram).

2.4.13 Investigate components of a good definition and be able to state equivalent definitions for various quadrilaterals.

2.4.14 Describe, identify, and draw sketches of other polygons (pentagons through dodecagons and n-gons).

2.4.15 Describe, identify, and draw sketches of polygons that are convex, concave, regular, equiangular, and equilateral.

2.4.16 Through investigation, deduce and apply properties of polygons such as the number of diagonals, the sum of interior and exterior angles, the measure of interior and exterior angles of regular polygons, etc.

2.4.17 Identify the reflectional and rotational symmetries of a polygon.

2.4.18 Describe, identify, and draw sketches of two or more circles that are: internally and externally tangent, and intersecting and concentric.

2.4.19 Identify and sketch segments, lines, and angles related to circles.

2.4.20 Through investigation, deduce and apply properties of angles, arcs, chords, secants, tangents, etc.

2.4.21 Identify whether two figures are congruent.

2.4.22 Through investigation, deduce and apply properties of congruent triangles: congruence of corresponding parts.

2.4.23 Use properties of congruent triangles to develop deductive reasoning skills.

2.4.24 Demonstrate, utilizing a variety of proof formats, the understanding of "necessary" and "sufficient" conditions.

2.4.25 Demonstrate, utilizing a variety of proof formats, understanding of methods for establishing triangle congruence – SSS, SAS, ASA, AAS, HL.

2.4.26 Apply properties of congruent triangles to establish validity of compass constructions.

2.4.27 Apply properties of ratios and proportions to solve for unknown quantities in real life problems.

2.4.28 Through investigation, deduce and apply properties of similar polygons: congruence of corresponding angles and proportionality of corresponding sides.

2.4.29 Use properties of similar triangles to develop deductive reasoning skills.

2.4.30 Demonstrate, utilizing a variety of proof formats, understanding of "necessary" and "sufficient" conditions.

2.4.31 Demonstrate, utilizing a variety of proof formats, understanding of methods for establishing triangle similarity – AAA, SSS, SAS.

2.4.32 Through investigation, deduce and apply properties of special right triangles.

2.4.33 Apply the Pythagorean Theorem to real-life problems and exhibit at least one proof of this theorem.

2.4.34 Apply basic trigonometric ratios in order to solve real-life problems.

2.5.2 Represent transformations in the plane using sketches, matrices, vectors, and functions.

2.5.3 Use rigid transformations to map congruent polygons onto one another.

2.5.4 Discuss the applications of rigid transformations.

2.5.5 Use technology, manipulatives, and coordinate geometry to explore, deduce, and apply properties of dilations.

2.5.6 Relate the properties of non-rigid transformations to similar polygons.

Art, design, and construction

2.6.2 Draw planar figures given particular measures.

2.6.3 Apply the properties of similar figures to linear and area measures.

2.6.4 Use manipulatives, technology, and formulas to determine the linear, area, and volume measures associated with: prisms, cylinders, pyramids, cones, and spheres.

2.6.5 Sketch solids given particular measures.

2.6.6 Describe the cross-section of various three-dimensional objects by visualizing the objects from various perspectives.

2.6.7 Apply the properties of similar solids to linear, area, and volume measures.

2.6.8 Represent two- and three-dimensional geometric objects using shadows, perspectives, projections, and nets.