G.1: The student will use deductive and inductive reasoning to solve problems.

G.1.1: Identify and use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, and follow logical arguments.

Biconditional Statements
Conditional Statements

G.2: The student will use the properties and formulas of geometric figures to solve problems.

G.2.1: Use geometric tools (for example, protractor, compass, straight edge) to construct a variety of figures.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

G.2.2: Line and Angle Relationships

G.2.2.a: Use the angle relationships formed by parallel lines cut by a transversal to solve problems.

Constructing Congruent Segments and Angles
Triangle Angle Sum

G.2.2.c: Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems.

Triangle Angle Sum

G.2.3: Polygons and Other Plane Figures

G.2.3.a: Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal).

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Polygon Angle Sum
Special Parallelograms

G.2.3.c: Develop and apply the properties of quadrilaterals to solve problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites).

Classifying Quadrilaterals
Parallelogram Conditions
Perimeter and Area of Rectangles
Special Parallelograms

G.2.4: Similarity

G.2.4.b: Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Similar Figures

G.2.5: Congruence

G.2.5.b: Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Circumference and Area of Circles

G.2.6: Circles

G.2.6.a: Find angle measures and arc measures related to circles.

Chords and Arcs
Inscribed Angles

G.2.6.b: Find angle measures and segment lengths using the relationships among radii, chords, secants, and tangents of a circle.

Chords and Arcs
Inscribed Angles

G.3: The student will use the properties of right triangles and trigonometric ratios to solve problems.

G.3.3: Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems.

Sine, Cosine, and Tangent Ratios

G.4: The student will use the properties and formulas of geometric figures to solve problems.

G.4.1: Polyhedra and Other Solids

G.4.1.b: Use properties of 3-dimensional figures; side lengths, perimeter or circumference, and area of a face; and volume, lateral area, and surface area to determine unknown values and correctly identify the appropriate unit of measure of each.

Surface and Lateral Areas of Prisms and Cylinders

G.4.3: Create a model of a 3-dimensional figure from a 2-dimensional drawing and make a 2-dimensional representation of a 3-dimensional object (for example, nets, blueprints, perspective drawings).

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

G.5: The student will solve problems with geometric figures in the coordinate plane.

G.5.1: Use coordinate geometry to find the distance between two points; the midpoint of a segment; and to calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.

Circles
Distance Formula
Point-Slope Form of a Line

G.5.2: Properties of Figures

G.5.2.b: Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.

Dilations