Although we may not always recognize it, we use basic geometry skills regularly in everyday life. For instance, we consider whether a picture on the wall is parallel with the floor, or we calculate the area of a room when installing new carpeting.
Geometry is also an integral part of many other areas of study, including physics and other natural sciences. This course provides a more rigorous mathematical foundation for both practical and theoretical geometric thinking.
The course begins by considering basic figures such as points, lines, and planes, and then expands into the concepts of parallelism and perpendicularity as well as more complicated geometric figures such as polygons (triangles, quadrilaterals, and so on) and circles. The course considers mainly two-dimensional figures, but two lessons on three-dimensional geometry provide more complete coverage of the subject.
Each successive lesson in the course builds on previous lessons, culminating in lessons that teach the student how to calculate lengths, areas, and volumes of more complicated figures. In addition to its in-depth discussion of the mathematical aspects of geometry, the course also includes lessons on how to draw various figures using a compass and straightedge as well as a lesson on strategy for solving real-world geometry problems.
The course concludes by applying all that the student has learned to a brief introduction to trigonometry, thereby providing a jumping-off point for a more rigorous study of geometry as well as other areas of mathematics. By the end of the course, the student should feel comfortable tackling a range of basic to moderately difficult geometry problems.
Course Goals
-Discuss why the study of geometry can be beneficial, both in school and work as well as in daily life.
-Review several fundamental terms and geometric figures
-Review some fundamental principles of geometric reasoning and measurement
-Discuss the concept of an angle and discuss the relationships among angles formed by intersecting lines.
-Introduce a fundamental definition of parallelism and then go on to identify some of the crucial properties of angles formed by parallel lines that are cut by a transversal line.
-Discuss different triangle shapes, right triangles and the Pythagorean theorem, and how we derive the formula for the area of a triangle.
-Discuss a number of conditions that can be used to prove that two triangles are congruent
-Discuss several criteria for proving that two triangles are similar.
-Study the basic properties of quadrilaterals and go on to identify special quadrilaterals and to derive formulas for their areas.
-Study the basic properties of n-sided polygons
-Discuss the properties and calculating corresponding values of a circle
-Study how to solve composite figures
-Learn simple "classical constructions" using a pencil, compass, and straightedge
-Learn how to solve practical geometry problems
-Study the principles and complexities of three-dimensional parallelism and perpendicularity
-How to calculate the volume and surface area, as well as some of the characteristics of three-dimensional figures.
-Introduce the study of trigonometry, which expands on our knowledge of circles, angles, triangles, and other aspects of geometry
Course Objectives
Lesson 1 - Geometry Terms and Motivation
Lesson 2 - Geometric Reasoning and Measurement
Lesson 3 - Angles and Parallelism
Lesson 4 - Triangles I: Properties of Triangles
Lesson 5 - Triangles II: Congruent Triangles
Lesson 6 - Triangles III: Similar Triangles
Lesson 7 - Quadrilaterals
Lesson 8 - Polygons
Lesson 9 - Circles
Lesson 10 - Composite Figures
Lesson 11 - Classical Construction
Lesson 12 - Practical Geometry Problems
Lesson 13 - Three-Dimensional Geometry I
Lesson 14 - Three-Dimensional Geometry II
Lesson 15 - Geometry and Trigonometry
