G.1: The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include

G.1.a: identifying the converse, inverse, and contrapositive of a conditional statement;

Biconditional Statements
Conditional Statements

G.2: The student will use the relationships between angles formed by two lines cut by a transversal to

G.2.a: determine whether two lines are parallel;

Constructing Congruent Segments and Angles

G.3: The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include

G.3.a: investigating and using formulas for finding distance, midpoint, and slope;

Circles
Distance Formula
Distance-Time and Velocity-Time Graphs
Parabolas
Point-Slope Form of a Line
Slope

G.3.b: applying slope to verify and determine whether lines are parallel or perpendicular;

Cat and Mouse (Modeling with Linear Systems)

G.3.c: investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and

Holiday Snowflake Designer

G.3.d: determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

Dilations
Rotations, Reflections, and Translations
Translations

G.4: The student will construct and justify the constructions of

G.4.a: a line segment congruent to a given line segment;

Constructing Congruent Segments and Angles

G.4.b: the perpendicular bisector of a line segment;

Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

G.4.c: a perpendicular to a given line from a point not on the line;

Constructing Parallel and Perpendicular Lines

G.4.d: a perpendicular to a given line at a given point on the line;

Constructing Parallel and Perpendicular Lines

G.4.e: the bisector of a given angle;

Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

G.4.f: an angle congruent to a given angle; and

Constructing Congruent Segments and Angles

G.4.g: a line parallel to a given line through a point not on the given line.

Constructing Parallel and Perpendicular Lines

G.5: These concepts will be considered in the context of real-world situations.The student, given information concerning the lengths of sides and/or measures of angles in triangles, will

G.5.c: determine whether a triangle exists; and

Classifying Triangles

G.7: The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs.

Similar Figures

G.8: The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios

G.11: The student will use angles, arcs, chords, tangents, and secants to

G.11.a: investigate, verify, and apply properties of circles;

Chords and Arcs
Inscribed Angles

G.11.c: find arc lengths and areas of sectors in circles.

Inscribed Angles

G.12: The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.

Circles

G.13: The student will use formulas for surface area and volume of three-dimensional objects to solve real-world problems.

Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

G.14: The student will use similar geometric objects in two- or three-dimensions to

G.14.a: compare ratios between side lengths, perimeters, areas, and volumes;

Perimeters and Areas of Similar Figures
Similar Figures

G.14.d: solve real-world problems about similar geometric objects.

Similar Figures