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High School Level—Geometry

Develop the ability to read, write, think, and communicate about the concepts of high school level geometry.
High School Level-Geometry is rated 4.5 out of 5 by 36.
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Rated 5 out of 5 by from Geometry as how it should be taught! James Noggle does not use any high tech methods to teach high school geometry. He clearly starts from the beginning using postulates and goes right into the theorems proving most of them. Using many examples on an old chalk board, you can clearly"reason" with him step by step. So this is not like somebody just putting up "slides" on a projector. Hearing the sound of chalk on the board working through a problem is reassuring that you see mathematics in the truest form. I believe this is how mathematics must be taught and I would like to see The Great Courses look for and find more gifted people like him. I was looking for a review of high school geometry and I found it. The work book is very good also. I will give James Noggle and A+ for a highly deserved presentation. The Great Courses should find an individual like him to teach high school calculus and advanced geometry.
Date published: 2016-04-13
Rated 4 out of 5 by from Classical teaching with chalkboard and flip charts It is still amazing what a few teachers can still do with chalkboard and flip charts in the era of sophisticated visual aids. Professor Noggle is a “master” for using these teaching classical methods. In addition, he is very methodic and didactic. However, I tend to agree with other reviewers that a re-edition of this course using better (visual aids) technology will improve this course. I would also like to recommend 6 additional lectures to cover more topics of trigonometry, such as basic trigonometric identities that are relevant in Calculus and Physics.
Date published: 2016-03-13
Rated 5 out of 5 by from Great course! Great course. Take this before you enroll in high school or college geometry. It teaches you everything you need to know to get through a first and probably second year of geometry. If you are having problems in your geometry class, you can always go back and watch these videos until you get a grasp of what you are having problems with. It is great to be able to pause the video and take notes. You could take these to class and add whatever you are being taught to them.
Date published: 2016-01-29
Rated 2 out of 5 by from Good content, Poor quality. I wouldn't be so picky if this didn't cost a foot and I never write reviews but this one deserves one and reasons why I haven't bought another great course in a year. I wish I could get my money back for this one, but it's too late. I beg of you to not buy this one and search for another updated Geometry course. I bought this a year ago, along with a great deal of other math courses all the way up to Calculus. I'm one of those people that like to have the whole package and wish to look this over all throughout my life. This review is based on QUALITY more than content where as I do believe if you try HARD enough to learn from this you will definitely succeed. My problem is how the video shows its date - like something born out of the 90's - and the instructor is writing on a chalkboard and paper. I wouldn't mind this if... I could see what he's writing sometimes. I have a brand new mac book pro so it isn't my hardware. Don't think I'm crazy, like I said if I didn't pay so much I wouldn't be picky. But look if you compare this to say.. James A Sellers courses and how he seamlessly throws information at you in a quick pace makes math fun and unrecognizable. This... Reminds me of my old high school teacher. *Shivers* And is a struggle to get through. I feel is this is ever updated and Great Courses would allow us to have that updated version for free, my trust in buying their courses will be restored. My advise, don't buy a course if it doesn't have a trailer ;) Quality matters when it comes to things like this. I guess I'm going to have to read through the written portion.
Date published: 2015-11-17
Rated 5 out of 5 by from Classic in every sense Even though the production technics are somewhat outdated, it's definitively a great introduction not only to Geometry, but to something often neglected: A training tool in deductive and inductive reasoning. After all, this is what many great minds such as Einstein admired from Euclid's Geometry which, as described by the Greek mathematician, is a monument to a great human achievement. In fact, Mathematic reasoning It's nice to know the formulas and resolve geometric problems, but is also at least equally important the great benefit of the discipline of rational and methodical thinking. My recommendation to the Teaching company is to call Professor Noggle if available and re-do the course a-la-Prof. Bruce Edwards and Prof. James Sellers and expand the course a little bit. The Teaching Company actually has a more recent Geometry course and I have both. However, if I am ever exiled to a virtual mathematical island and I must take either one and only one, I will select Prof. Noggle's Geometry. I think I would never regret it. I highly recommend it.
Date published: 2015-01-16
Rated 3 out of 5 by from 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.
Date published: 2014-06-02
Rated 4 out of 5 by from 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?
Date published: 2014-03-26
Rated 5 out of 5 by from 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.
Date published: 2014-01-13
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Overview

Professor Noggle's lectures on geometry are exceptionally clear and well organized. He has an evident love for the topic, and a real gift for conveying the elegance and precision of geometric concepts and demonstrations. You will learn how geometrical concepts link new theorems and ideas to previous ones. This helps you see geometry as a unified body of knowledge whose concepts build upon one another.

About

James Noggle

We will start out with the basic ideas of helping you try to visualize the relationships of points and lines and planes in space and how these things work together and interact with each other.

INSTITUTION

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.

Fundamental Geometric Concepts

01: 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.

33 min
Angles and Angle Measure

02: 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.

31 min
Inductive Reasoning and Deductive Reasoning

03: 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.

32 min
Preparing Logical Reasons for a Two-Column Proof

04: 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.

31 min
Planning Proofs in Geometry

05: 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.

32 min
Parallel Lines and Planes

06: 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.

31 min
Triangles

07: Triangles

We classify triangles according to their sides and angles, and use theorems about the angles of a triangle.

32 min
Polygons and Their Angles

08: 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.

31 min
Congruence of Triangles

09: 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.

31 min
Variations of Congruent Triangles

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.

30 min
More Theorems Related to Congruent Triangles

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.

31 min
Median, Altitudes, Perpendicular Bisectors, and Angle Bisectors

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.

31 min
Parallelograms

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.

31 min
Rectangles, Rhombuses, and Squares

14: Rectangles, Rhombuses, and Squares

We identify rectangles, rhombuses, and squares; and state and apply properties and theorems related to their properties.

31 min
Trapezoids, Isosceles Trapezoids, and Kites

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.

31 min
Inequalities in Geometry

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.

31 min
Ratio, Proportion, and Similarity

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.

31 min
Similar Triangles

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.

32 min
Right Triangles and the Pythagorean Theorem

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.

31 min
Special Right Triangles

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.

30 min
Right-Triangle Trigonometry

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.

31 min
Applications of Trigonometry in Geometry

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.

32 min
Tangents, Arcs, and Chords of a Circle

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.

31 min
Angles and Segments of a Circle

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.

30 min
The Circle as a Whole and Its Parts

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.

31 min
The Logic of Constructions through Applied Theorems (Part I)

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.

30 min
The Logic of Constructions through Applied Theorems (Part II)

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.

31 min
Areas of Polygons

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.

31 min
Prisms, Pyramids, and Polyhedra

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.

32 min
Cylinders, Cones, and Spheres

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.

31 min