Geometry (Period 8)

This course will cover plane Euclidean geometry; coordinate geometry and its transformations; developing formal, logical arguments and proofs; and geometric constructions with a straightedge and compass. Proofs are usually the intimidating aspect of geometry. It should be noted that only trial and error can lead to a correct proof.

In this course, students will know and be able to:
• Identify and give examples of undefined terms, axioms, theorems, inductive and deductive reasoning
• Construct and judge the validity of a logical argument and give counterexamples to disprove a statement
• Write geometric proofs, including proofs by contradiction
• Prove basic theorems involving congruence and similarity
• Prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals and the properties of circles
• Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
• Prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles and inscribed and circumscribed polygons of circles
• Prove the Pythagorean Theorem
• Derive and solve problems involving perimeter, circumference, area, volume, lateral area and surface area of common geometric figures
• Compute areas of polygons
• Know the definitions of the basic trigonometric functions defined by the angles of a right triangle, and the elementary relationships between them
• Use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side
• Prove theorems involving coordinate geometry
• Know the effect of rigid motions on figures in the coordinate plane and space