**Автор**: James Noggle \ Джеймс Ногл

**Страна**: США

**Жанр**: Лекции

**Издательство**: The Teaching Company

**Язык**: английский

**Продолжительность**: 30 лекций по 30 минут

**Описание**: Лекции по геометрии для средней школы.

**Course Lecture Titles**

1. Fundamental Geometric Concepts

2. Angles and Angle Measure

3. Inductive Reasoning and Deductive Reasoning

4. Preparing Logical Reasons for a Two-Column Proof

5. Planning Proofs in Geometry

6. Parallel Lines and Planes

7. Triangles

8. Polygons and Their Angles

9. Congruence of Triangles

10. Variations of Congruent Triangles

11. More Theorems Related to Congruent Triangles

12. Median, Altitudes, Perpendicular Bisectors, and Angle Bisectors

13. Parallelograms

14. Rectangles, Rhombuses, and Squares

15. Trapezoids, Isosceles Trapezoids, and Kites

16. Inequalities in Geometry

17. Ratio, Proportion, and Similarity

18. Similar Triangles

19. Right Triangles and the Pythagorean Theorem

20. Special Right Triangles

21. Right-Triangle Trigonometry

22. Applications of Trigonometry in Geometry

23. Tangents, Arcs, and Chords of a Circle

24. Angles and Segments of a Circle

25. The Circle as a Whole and Its Parts

26. The Logic of Constructions through Applied Theorems (Part I)

27. The Logic of Constructions through Applied Theorems (Part II)

28. Areas of Polygons

29. Prisms, Pyramids, and Polyhedra

30. Cylinders, Cones, and Spheres

**Описание на английском языке**

For more than 30 years Professor James Noggle has been letting his students in on a secret at the high school in Pendleton, Indiana. He makes geometry feel like a long, cool drink as he guides you through the mysteries of lines, planes, angles, inductive and deductive reasoning, parallel lines and planes, triangles, polygons, and more.

In this course taught by an award-winning teacher, you develop the ability to read, write, think, and communicate about the concepts of geometry. As your comprehension and understanding of the geometrical vocabulary increase, you will have the ability to explain answers, justify mathematical reasoning, and describe problem-solving strategies.

Professor Noggle relies heavily on the blackboard and a flipchart on an easel in his 30 lectures. Very little use is made of computer-generated graphics, though several physical models of geometric objects are used throughout the lectures.

A New Way to Look at the World around You

The language of geometry is beautifully expressed in words, symbols, formulas, postulates, and theorems. These are the dynamic tools by which you can solve problems, communicate, and express geometrical ideas and concepts.

Connecting the geometrical concepts includes linking new theorems and ideas to previous ones. This helps you to see geometry as a unified body of knowledge whose concepts build upon one another. And you should be able to connect these concepts to appropriate real-world applications.

Professor Noggle’s Geometry course will begin with basic fundamental concepts used throughout the course. Students will be able to recognize and define such terms as points, planes, and angles; parallel lines, skew lines, parallel planes, and transversals; as well as the terms space, collinear, intersection, segment, and ray.

Students will discover the world of angles—symbols used for them, establishing a system of angle measurement, classifying the different types, and showing angle relationships.

The course then continues with the use of inductive reasoning to discover mathematical relationships and recognize real-world applications of inductive reasoning, conditional statements, and deductive reasoning.

Using the Fundamental Tools of Geometry

After the first few lectures introduce students to the basic terms, Professor Noggle will open the world of geometry to students. Upon completion of this course, you should be able to:

Classify triangles according to their sides and angles

Distinguish between convex polygons and concave polygons, and find the interior and exterior angles of convex polygons

State and apply postulates and theorems involving parallel lines and convex polygons to solve related problems and prove statements using deductive reasoning.

Explain the ratio in its simplest form; identify, write, and solve proportions

Identify congruent parts of congruent triangles; state and apply the SSS, SAS, and ASA postulates; and use those postulates to prove triangles congruent

Be able to define, state, and apply theorems for parallelograms, rectangles, rhombuses, squares, and trapezoids

Apply proportions and concepts of proportionality in right triangles; discuss the Pythagorean Theorem

Explore the relationships between right and isosceles triangles

Define tangent, sine, and cosine rations for angles

State and apply properties and theorems regarding circles and their tangents, chords, central angles, and arcs

Address the derivation of the area formulas and apply those formulas to rectangles, squares, parallelograms, triangles, trapezoids, and regular polygons

Define polyhedron, prism, pyramid, cylinder, cone, and sphere; and apply theorems to compute the lateral area, total area, and volume of the prism, pyramid, cylinders, cones, and spheres.

**The Teaching Company**

The Teaching Company was founded in 1990 by Thomas M. Rollins, former Chief Counsel of the United States Senate Committee on Labor and Human Resources.

Years earlier, as a Harvard Law School student, Rollins had an unforgettable experience that opened his eyes to the extraordinary power of a great lecturer captured on tape.

Rollins was facing an important exam in the Federal Rules of Evidence but was not well prepared. He managed to obtain videotapes of 10 one-hour lectures by a noted authority on the subject, Professor Irving Younger.

"I dreaded what seemed certain to be boring," Rollins says. "I thought that few subjects could be as dull as the Federal Rules of Evidence. But I had no other way out."

Rollins planted himself in front of the TV and played all 10 hours nearly non-stop. The lectures, he says, "were outrageously insightful, funny, and thorough." Watching Professor Younger's lectures was one of Rollins's best experiences as a student.

Rollins made an "A" in the course. And he never forgot the unique power of recorded lectures by a great teacher.

After many years of government service, Rollins founded The Teaching Company in 1990 to ignite people's passion for lifelong learning by offering great courses taught by great professors.

**Релиз группы:**

**Качество**: DVDRip

**Формат**: AVI

**Видео кодек**: XviD

**Аудио кодек**: MP3

**Видео**: 400 х 288, 29.97fps

**Аудио**: 48KHz Stereo 128 kbps

**Скриншоты**