About This Chapter
How it works:
- Identify the lessons in your textbook chapter with which you need help.
- Find the corresponding video lessons within this online chapter.
- Watch fun videos that cover the Pythagorean theorem topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- How to apply the Pythagorean theorem
- Special cases where the Pythagorean theorem is used
- Types of special right triangles
- How to calculate the distance for Pythagorean theorems
- How to figure out the distance formula
- Ways to identify graphing circles
- How to solve the area for right triangles, circles and tangent lines
1. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
2. The Pythagorean Theorem: Converse and Special Cases
The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.
3. Special Right Triangles: Types and Properties
Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.
4. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
5. How to Use The Distance Formula
You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!
6. Graphing Circles: Identifying the Formula, Center and Radius
Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.
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Other chapters within the Discovering Geometry An Investigative Approach: Online Help course
- Discovering Geometry Chapter 1: Introducing Geometry
- Discovering Geometry Chapter 2: Reasoning in Geometry
- Discovering Geometry Chapter 3: Using Tools of Geometry
- Discovering Geometry Chapter 4: Discovering and Proving Triangle Properties
- Discovering Geometry Chapter 5: Discovering and Proving Polygon Properties
- Discovering Geometry Chapter 6: Discovering and Proving Circle Properties
- Discovering Geometry Chapter 7: Transformations and Tessellations
- Discovering Geometry Chapter 8: Area
- Discovering Geometry Chapter 10: Volume
- Discovering Geometry Chapter 11: Similarity
- Discovering Geometry Chapter 12: Trigonometry
- Discovering Geometry Chapter 13: Geometry as a Mathematical System