TTC Video - High School Level - Geometry

by Nguyen Trung Hoa Sun 22 Aug 2010, 7:20 am

TTC Video - High School Level - Geometry-with Guide Book

(30 lectures, 30 minutes/lecture)
Course No. 105

Taught by James Noggle
Pendleton Heights High School, Pendleton, Indiana
M.Ed., Ball State University

For over 30 years 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 award-winning teacher James Noggle, 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.

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.

Mr. 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.

Upon completion of Geometry, you should be able to:

1. State and apply postulates and theorems related to points, lines, planes, and angles and use symbols to name and draw representations of them.
2. State and apply components of deductive reasoning to investigate relationships, solve problems, and prove statements.
3. State and apply postulates and theorems involving parallel lines and convex polygons to solve related problems and prove statements using deductive reasoning.
4. State and apply postulates and theorems related to congruent polygons to prove triangles and/or their corresponding parts congruent.
5. State and apply definitions, properties, and postulates to identify different quadrilaterals and prove statements about them.
6. State and apply components of logic and indirect proof to investigate inequities in triangles.
7. State and apply definitions, properties, postulates, and theorems related to similar polygons to prove triangles similar using deductive reasoning and to deduce information about segments or angles.
8. State and apply properties, postulates, and theorems related to right triangles to deduce relationships and solve for missing information in diagrams.
9. State and apply definitions, properties, postulates, and theorems about circles and terms related to circles to solve problems and prove statements using deductive reasoning.
10. Use compass, straight edge, and previously learned relationships to construct simple geometric figures.
11. State and apply formulas for finding area and volume for plane figures.
12. State and apply formulas for finding surface area and volume for simple solids.

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

Full size: ~5,2Gb.

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