Given conjectures about quadrilaterals, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

Given problem situations involving similar figures, the student will apply and justify triangle similarity relationships such as trigonometric ratios.

The student will derive and use the slope and midpoint formulas to verify geometric relationship that include parallelism and perpendicularity of lines. Then, the student will determine an equation of a line parallel or perpendicular to a given line.

Given a figure, the student will identify the scale factor used for a dilation, and use a dilation by a scale factor, including enlargements and reductions, to generate similar figures.

Given examples of triangles and their component parts, the student will use explorations and concrete models to verify and apply the Triangle Inequality theorem and find the sum of interior angles.

Given a problem situation, the student will evaluate a method of sampling to determine the validity of an inference made from the set of data.

Given coordinates of points, the student will use the distance formula to solve problems involving length and distance.

Given pictorial representations, the student will use geometric concepts and properties to solve problems from art and architecture.

Given problems that include data, the student will generate different representations, such as a table, graph, equation, or verbal description.

Given data in the form of a graph, the student will use the graph to interpret solutions to problems.