About This Chapter
How it works:
- Identify the lessons in the Discovering Geometry Reasoning in Geometry chapter with which you need help.
- Find the corresponding video lessons within this online chapter.
- Watch fun videos that cover the reasoning in geometry 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:
- Inductive and deductive reasoning
- Mathematical inductions
- Geometric sequences
- Mathematical sequences
- Special sequences
- Logic and critical thinking in math
- The meaning of converse of a statement
- Linear pairs
- Complementary and vertical angles
- Alternate interior, vertical and corresponding angles
- When to use converse statements
1. Inductive & Deductive Reasoning in Geometry: Definition & Uses
Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.
2. Mathematical Induction: Uses & Proofs
Watch this video lesson to learn about mathematical induction and how you can use it to prove mathematical statements. See how it is similar to falling dominoes.
3. Working with Geometric Sequences
In this video lesson, we'll learn how to recognize when a sequence of numbers is a geometric sequence, how to find the common ratio and how to expand a sequence to as many numbers as we want!
4. What is a Mathematical Sequence?
Math is often the most fun when it acts like a puzzle to be solved. The branch of math where this is the most true involves sequences. Get an introduction to the basics and important vocabulary, as well as learn where sequences appear in nature!
5. Special Sequences and How They Are Generated
Sequences are interesting things in math and in nature. The most interesting thing is that these sequences have a pattern to how they are generated. We will learn about a few of them in this video lesson.
6. Critical Thinking and Logic in Mathematics
Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.
7. Converse of a Statement: Explanation and Example
Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.
8. Vertical Angles & Complementary Angles: Definition & Examples
Special angles make your life easier. Learn how you can use the properties of special angles to help you find the measurements of missing angles in this video lesson.
9. Types of Angles: Vertical, Corresponding, Alternate Interior & Others
In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.
10. Using Converse Statements to Prove Lines Are Parallel
Because a pair of parallel lines produces unique angle characteristics, we can use this information to our advantage. Watch this video lesson to see how we turn this advantage into converse statements to help us prove parallel lines.
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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 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 9: The Pythagorean Theorem
- Discovering Geometry Chapter 10: Volume
- Discovering Geometry Chapter 11: Similarity
- Discovering Geometry Chapter 12: Trigonometry
- Discovering Geometry Chapter 13: Geometry as a Mathematical System