Geometry
College
Course Outline
Course Description:
This course presents the fundamentals of plane, solid and nonEuclidean geometries. Topics include the history of mathematical thought and reasoning, measurement, congruence, similarity, parallelism, perpendicularity, and methods of proof.
Course Outline:

Line and Angle Relationships

Sets, Statements and Reasoning

Informal Geometry and Measurement

Early Definitions and Postulates

Angles and Their Relationships

Introduction to Geometric Proof

Relationships: Perpendicular Lines

The Formal Proof of a Theorem

Parallel Lines

The Parallel Postulate and special Angles

Indirect Proof

Proving Lines Parallel

The Angles of a Triangle

Convex Polygons

Triangles

Congruent Triangles

Corresponding Parts of Congruent Triangles

Isosceles Triangles

Basic Constructions Justified

Inequalities in a Triangle

Quadrilaterals

Properties of Parallelograms

The Parallelogram and Kite

The Rectangle, Square, and Rhombus

The Trapezoid

Similar Triangles

Ratios, Rates, and Proportions

Similar Polygons

Proving Triangles Similar

The Pythagorean Theorem

Special Right Triangles

Segments Divided Proportionally

Circles

Circles and related Segments and Angles

More Angle Measures in the Circle

Areas of Polygons and Circles

Area and Initial Postulates

Perimeter and Area of Polygons

Circumference and Area of a Circle

Surfaces and Solids (if time permits)

Prisms, Area and Volume

Pyramids, Area and Volume

Cylinders and Cones

Polyhedrons and Spheres