Essential Question:  How can the properties of polygons be used to identify and prove theorems?

Unit Rationale:  Extending the properties and theorems of triangles to convex polygons expands our ability to prove and apply conjectures about a wider number of two-dimensional physical shapes and prepare us for future applications of three-dimensional shapes, such as prisms and pyramids.

As a result of this unit, students will be able to:

Ø  Determine the sum of the measures of the interior angles of any polygon and the measure of each angle in a regular polygon.

Ø  Apply the knowledge that the sum of the exterior angles of a polygon is constant at 360 degrees.

Ø  Identify, prove, and apply the properties of general and special quadrilaterals.

Vocabulary:

·        Quadrilateral

·        Kite

·        Trapezoid

·        Parallelogram

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

G.2.A  Know, prove, and apply theorems about parallel and perpendicular lines.

G.2.B  Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.

*G.3.F  Know, prove, and apply basic theorems about parallelograms.

*G.3.G  Know, prove, and apply theorems about properties of quadrilaterals and other polygons.

G.4.A  Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a give point parallel to a given line, and a line through a given point perpendicular to a given line.

*G.4.B  Determine coordinates of a point that is described geometrically.

Supporting Standards:

G.1.B  Use inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counterexample.

*G.1.C  Use deductive reasoning to prove that a valid geometric statement is true.

*G.4.C  Verify and apply properties of triangles and quadrilaterals in the coordinate plane.

Reasoning, Problem Solving, and Communication Standards:

G.7.D  Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class of related problems to solve specific problems.

*G.7.G  Synthesize information to draw conclusions and evaluate the argument and conclusions of others.