LG.1.G: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

LG.1.G.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations

LG.1.G.1.c: conditional statements (statement, inverse, converse, and contrapositive)

Biconditional Statements
Conditional Statements

LG.1.G.3: Describe relationships derived from geometric figures or figural patterns

Finding Patterns

LG.1.G.4: Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Investigating Angle Theorems
Triangle Angle Sum

LG.1.G.5: Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

Constructing Congruent Segments and Angles
Triangle Angle Sum

LG.1.G.6: Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180° , and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it?s length

Conditional Statements
Investigating Angle Theorems
Isosceles and Equilateral Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum

T.2.G: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.

T.2.G.1: Apply congruence (SSS ?) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

Circles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

T.2.G.2: Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

Triangle Inequalities

T.2.G.3: Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Similarity in Right Triangles

T.2.G.4: Apply the Pythagorean Theorem and its converse in solving practical problems

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

T.2.G.5: Use the special right triangle relationships (30°-60°-90° and 45°-45°-90°) to solve problems

Cosine Function
Sine Function
Tangent Function

T.2.G.6: Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

T.2.G.7: Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given including angles of elevation and angles of depression

Sine, Cosine, and Tangent Ratios

M.3.G: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.

M.3.G.1: Calculate probabilities arising in geometric contexts

Geometric Probability

M.3.G.2: Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

M.3.G.4: Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)

Beam to Moon (Ratios and Proportions)
Dilations

R.4.G: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

R.4.G.1: Explore and verify the properties of quadrilaterals

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

R.4.G.2: Solve problems using properties of polygons:

R.4.G.2.a: sum of the measures of the interior angles of a polygon

Polygon Angle Sum
Triangle Angle Sum

R.4.G.2.b: interior and exterior angle measure of a regular polygon or irregular polygon

Polygon Angle Sum

R.4.G.2.c: number of sides or angles of a polygon

Polygon Angle Sum

R.4.G.5: Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

Chords and Arcs
Inscribed Angles

R.4.G.6: Solve problems using inscribed and circumscribed figures

Concurrent Lines, Medians, and Altitudes
Inscribed Angles

R.4.G.7: Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects

3D and Orthographic Views

CGT.5.G: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

CGT.5.G.1: Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

Point-Slope Form of a Line

CGT.5.G.6: Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

Circles

CGT.5.G.7: Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane

CGT.5.G.7.a: translations

Rotations, Reflections, and Translations
Translations

CGT.5.G.7.b: reflections

Reflections
Rotations, Reflections, and Translations

CGT.5.G.7.c: rotations (90°, 180°, clockwise and counterclockwise about the origin)

Dilations
Rotations, Reflections, and Translations

CGT.5.G.7.d: dilations (scale factor)

Dilations
Similar Figures