M.O.G.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.G.3.8: identify general properties of and compare and contrast the properties of convex and concave quadrilaterals

M.O.G.3.8.a: parallelograms

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

M.O.G.3.8.b: rectangles

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

M.O.G.3.8.c: rhombuses

Classifying Quadrilaterals
Special Parallelograms

M.O.G.3.8.d: squares

Classifying Quadrilaterals
Perimeter and Area of Rectangles
Special Parallelograms

M.O.G.3.8.e: trapezoids

Classifying Quadrilaterals

M.O.G.3.9: identify a real life situation that involves similarity in two or three dimensions; pose a question; make a hypothesis as to the answer, develop, justify, and implement a method to collect, organize, and analyze related data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra and geometry (with and without technology).

Circles

M.O.G.3.10: investigate measures of angles and lengths of segments to determine the existence of a triangle (triangle inequality) and to establish the relationship between the measures of the angles and the length of the sides (with and without technology).

Concurrent Lines, Medians, and Altitudes

M.O.G.3.11: verify and justify the basis for the trigonometric ratios by applying properties of similar triangles and use the results to find inaccessible heights and distances. Using the ratios of similar triangles to find unknown side lengths and angle measures, construct a physical model that illustrates the use of a scale drawing in a real-world situation.

Beam to Moon (Ratios and Proportions)
Cosine Function
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

M.O.G.3.12: apply the Pythagorean Theorem and its converse to solve real-world problems and derive the special right triangle relationships (i.e. 30-60-90, 45-45-90).

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

M.O.G.3.13: investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.

Chords and Arcs
Inscribed Angles

M.O.G.3.14: find angle measures of interior and exterior angles; given a polygon, find the length of sides from given data; and use properties of regular polygons to find any unknown measurements of sides or angles.

Similar Figures
Triangle Angle Sum

M.O.G.3.16: derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.

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

M.O.G.3.18: construct a triangle?s medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.

Concurrent Lines, Medians, and Altitudes
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

M.O.G.3.19: create and apply concepts using transformational geometry and laws of symmetry, of a reflection, translation, rotation, glide reflection, dilation of a figure, and develop logical arguments for congruency and similarity.

Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations