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High School Level-Geometry

High School Level-Geometry

Professor James Noggle M.A.E.
Pendleton Heights High School, Pendleton, Indiana

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High School Level-Geometry

High School Level-Geometry

Professor James Noggle M.A.E.
Pendleton Heights High School, Pendleton, Indiana
Course No.  105
Course No.  105
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Course Overview

About This Course

30 lectures  |  31 minutes per lecture

Note: This course is now discontinued. Please see our new geometry course, Geometry: An Interactive Journey to Mastery.

For more than 30 years, Professor James Noggle has been letting his students in on the secret to making the mysteries of lines, planes, angles, inductive and deductive reasoning, parallel lines and planes, triangles, polygons, and other geometric concepts easy to grasp. And in his course, Geometry, you'll 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.

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Note: This course is now discontinued. Please see our new geometry course, Geometry: An Interactive Journey to Mastery.

For more than 30 years, Professor James Noggle has been letting his students in on the secret to making the mysteries of lines, planes, angles, inductive and deductive reasoning, parallel lines and planes, triangles, polygons, and other geometric concepts easy to grasp. And in his course, Geometry, you'll 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.
View Less
30 Lectures
  • 1
    Fundamental Geometric Concepts
    In this introductory lesson, we define point, line, and plane; use and understand the terms space, collinear, intersection, segment, and ray; learn terminology of various expressions relative to points, lines, and planes; and establish a system of linear measurement. x
  • 2
    Angles and Angle Measure
    We explore the definition of an angle and learn its parts; establish a system of angle measurement; recognize and classify types of angles; and show angle relationships. x
  • 3
    Inductive Reasoning and Deductive Reasoning
    We use inductive reasoning to discover mathematical relationships, recognize real-world applications of inductive reasoning, and understand conditional statements and deductive reasoning. x
  • 4
    Preparing Logical Reasons for a Two-Column Proof
    We review properties of equality for real numbers; summarize and review postulates related to points, lines, planes, and angles; and introduce new theorems related to points, lines, planes, and angles. x
  • 5
    Planning Proofs in Geometry
    We discuss the key elements of a two-column proof; learn how to draw and label a diagram for a proof; write a plan for the proof; use strategy to write a two-column proof; and write a two-column proof. x
  • 6
    Parallel Lines and Planes
    We identify parallel lines, skew lines, parallel planes, transversals, and the angles formed by them; and we state and apply postulates and theorems about angles formed when parallel lines are intersected by a transversal. x
  • 7
    Triangles
    We classify triangles according to their sides and angles, and use theorems about the angles of a triangle. x
  • 8
    Polygons and Their Angles
    We distinguish between convex polygons and concave polygons; name convex and regular polygons; and find measures of interior and exterior angles of convex polygons. x
  • 9
    Congruence of Triangles
    We identify congruent parts of congruent triangles; state and apply the SSS, SAS, and ASA postulates; and use those postulates to prove triangles congruent. x
  • 10
    Variations of Congruent Triangles
    We deduce that segments or angles are congruent by first proving two triangles congruent; use two congruent triangles to prove other, related facts; and prove two triangles congruent by first proving two other triangles congruent. x
  • 11
    More Theorems Related to Congruent Triangles
    We use the isosceles triangle theorem, its converse, and related theorems; and use the AAS theorem and right triangle theorems to prove triangles congruent. x
  • 12
    Median, Altitudes, Perpendicular Bisectors, and Angle Bisectors
    We discuss definitions of median, altitude, perpendicular bisector, angle bisector, and related terms; state and apply theorems related to them; and learn their points of concurrence. x
  • 13
    Parallelograms
    We state and apply the definition of a parallelogram, state and apply theorems related to the properties of a parallelogram, and prove that certain quadrilaterals are parallelograms. x
  • 14
    Rectangles, Rhombuses, and Squares
    We identify rectangles, rhombuses, and squares; and state and apply properties and theorems related to their properties. x
  • 15
    Trapezoids, Isosceles Trapezoids, and Kites
    We learn to identify trapezoids, isosceles trapezoids, and kites, and we state and apply properties and theorems related to them. x
  • 16
    Inequalities in Geometry
    We review properties of inequality for real numbers and relate them to segments and angles; state and apply the inequality relations for one triangle and for two triangles. x
  • 17
    Ratio, Proportion, and Similarity
    In this lesson we explain how to express a ratio in its simplest form; identify, write, and solve proportions; use ratios and proportions to solve problems; express a given proportion in other equivalent forms; and apply the properties of similar polygons using ratios and proportions. x
  • 18
    Similar Triangles
    We state and apply the AA Similarity Postulate, the SAS Similarity Theorem, and the SSS Similarity Theorem. We learn to solve for unknown measurements using the new postulates and theorems related to similarity and to apply the Triangle Proportionality Theorem, the Triangle Angle-Bisector Theorem, and related theorems. x
  • 19
    Right Triangles and the Pythagorean Theorem
    We apply proportions and the concepts of proportionality in right triangles, use and apply the geometric mean between two values, state and apply the relationships that exist when the altitude of a triangle is drawn to the hypotenuse, state and apply the Pythagorean Theorem and its converse, and relate the Pythagorean Theorem to inequalities. x
  • 20
    Special Right Triangles
    We explore how to apply relationships in a 45°-45°-90° right triangle and in a 30°-60°-90° right triangle and use those relationships in the development of the unit circle. x
  • 21
    Right-Triangle Trigonometry
    We define and apply the tangent, sine, and cosine ratios for an acute angle and solve right-triangle problems using those ratios. x
  • 22
    Applications of Trigonometry in Geometry
    We address how to select the correct trigonometric ratio to use in problem solving, and how to use trigonometry to solve real-life problems. x
  • 23
    Tangents, Arcs, and Chords of a Circle
    We apply basic definitions and concepts related to circles, and state and apply properties and theorems regarding circles and their tangents, chords, central angles, and arcs. x
  • 24
    Angles and Segments of a Circle
    We apply basic definitions and theorems related to inscribed angles; state and apply theorems involving angles with vertices not on the circle formed by tangents, chords, and secants; and state and apply theorems involving lengths of chords, secant segments, and tangent segments. x
  • 25
    The Circle as a Whole and Its Parts
    We state and apply the formulas for the circumference and area of a circle, and for the arc lengths and the areas of sectors of a circle. x
  • 26
    The Logic of Constructions through Applied Theorems (Part I)
    In sample exercises, we review lessons and solve problems having to do with segments, angles, parallel and perpendicular lines, circles and arcs, and others. x
  • 27
    The Logic of Constructions through Applied Theorems (Part II)
    Continuing sample exercises, we review lessons and solve problems having to do with triangles, isosceles triangles, proportions, hexagons, and others. x
  • 28
    Areas of Polygons
    We address the derivation of the area formulas and apply those formulas to find the areas of a rectangle, square, parallelogram, triangle, trapezoid, and regular polygon. x
  • 29
    Prisms, Pyramids, and Polyhedra
    We explore definitions of a polyhedron, prism, pyramid, and related terms; understand the logical derivation of area and volume formulas; and apply theorems to compute the lateral area, total area, and volume of prisms and pyramids. x
  • 30
    Cylinders, Cones, and Spheres
    We explain the definitions of cylinder, cone, and sphere; explain the logical derivation of area and volume formulas; and apply theorems to compute the lateral areas, total areas, and volumes of cylinders, cones, and spheres. x

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James Noggle
M.A.E. James Noggle
Pendleton Heights High School, Pendleton, Indiana
Professor James Noggle is a math instructor at Pendleton Heights High School in Pendleton, Indiana, where he has been teaching for more than 30 years. The math courses in which he has specialized are algebra I, geometry, trigonometry, and analytical geometry. This range of courses has enabled him to help his students see a broader view of their math and relate it in many ways to the uses in applications at more advanced levels. Professor Noggle graduated from Anderson University in Anderson, Indiana, with a math major, and he earned his M.A.E. with a math major from Ball State University. He is the recipient of Tandy Technology Scholar Award for academic excellence in mathematics, science, and computer science.
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Reviews

Rated 4.6 out of 5 by 30 reviewers.
Rated 5 out of 5 by Excellent Introduction or Review of Geometry Professor James Noggle’s “High School Geometry” is an excellent course whether you want an introduction to the subject or just need a review. He logically develops the necessary definitions, postulates, and theorems in a manner that vividly illustrates the method by which mathematics is systematically built. While some might criticize the course as being outdated or in need of more current visual aids, Noggle illustrates why an outstanding instructor with a chalkboard and flip chart easily trumps a lesser teacher who possesses all the latest aids and supporting materials. I noticed TTC has recently updated its Algebra I and Algebra II courses primarily by increasing the number of lectures from 30 to 36 in order to cover additional topics. If TTC chooses to increase the number of lectures in this course, I would recommend the six additional lectures include one lecture on truth tables, one on indirect proof, one on tessellations, and three on additional examples of formal two-column deductive proofs. Increased attention to two-column proofs could include more examples in the areas of triangles, quadrilaterals, and circles. November 11, 2011
Rated 3 out of 5 by The Course Covers the Basics My daughter used these lessons to supplement her geometry course this semester in high school. She watched most of the lessons, and I watched several with her. This review reflects our shared judgment. The good part is that the teacher does indeed give adequate and broad coverage to the main topics in geometry. There were a few areas where she found the teaching helpful, especially in proofs and theorems generally, as well as in circles. On the critical side, she found that he sometimes went on too long in basic matters but rushed too quickly through more complex material. Further, the feeling here was that the teacher was too dry and matter-of-fact, as opposed to interesting and captivating. While I am sort of a "just the facts, ma'am" sort of person myself, I sympathize with my daughter's desire to have teaching that is more exciting than this, especially in math and science. So, we grade the course average. June 1, 2014
Rated 4 out of 5 by In need of a second edition Professor Noggle is interesting and know how to make his teaching easy to understand. But this course is definitely one of the first of the Teaching Company and need to be refresh. The presentation is a little bit outdated, as well as the picture and sound quality. Is a second edition is in project? March 26, 2014
Rated 5 out of 5 by Geometry Basics on Steriods Professor Noggle hits the subject out of the park. I think his presentation is awesome and compelling. I could not wait to get to the next lesson. His presentation is clear and concise. He makes a couple of tiny errors but catches them himself and doesn´t miss a beat. And as he says...you can rewind and repeat. Totally impressive and essential for basics. January 13, 2014
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