Given verbal and pictorial representations of problem situations, the student will apply patterns from right triangles whose sides are Pythagorean Triples to solve the problems.

Students will investigate patterns and make conjectures about geometric relationships, including interior angles of polygons.

The student will apply the formula for the area of regular polygons to solve problems.

The student will use triangle relationships to prove the Pythagorean Theorem and solve problems.

Given information about the relationship(s) witnin one circle or a set of circles, the student will explore special segments and angles of circles.

Given coordinate points, the student will use slope formulas to solve problems.

Given coordinate points the student will use midpoint formulas to solve problems.

The students will use multiple representations of undefined terms on a coordinate plane to solve problems.

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