G.1.0: Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.

Simplifying Trigonometric Expressions

G.4.0: Students prove basic theorems involving congruence and similarity.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G.5.0: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.6.0: Students know and are able to use the triangle inequality theorem.

Triangle Inequalities

G.7.0: Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.

Investigating Angle Theorems - Activity A
Parallelogram Conditions

G.8.0: Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.9.0: Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders

G.10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

Area of Parallelograms - Activity A
Rectangle: Perimeter and Area

G.11.0: Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area

G.12.0: Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.

Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

G.13.0: Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

G.14.0: Students prove the Pythagorean theorem.

Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity B

G.15.0: Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

G.16.0: Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G.17.0: Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.

Distance Formula - Activity A
Pythagorean Theorem - Activity B

G.18.0: Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))² + (cos(x))² = 1.

Simplifying Trigonometric Expressions
Sine and Cosine Ratios - Activity A

G.19.0: Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.

Sine Function
Sine and Cosine Ratios - Activity A
Tangent Function

G.21.0: Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

Chords and Arcs
Inscribing Angles

G.22.0: Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.

Dilations
Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations