**Unit 2: REASONING IN GEOMETRY**

**CONCEPT: Visualization***:*

**ESSENTIAL QUESTIONS**How do you use inductive and deductive reasoning in geometry?

What is the underlying pattern within a problem?

How can I evaluate a sequence and then write an equation to represent it?

In this unit, you learn how to use a different kind of reasoning than in other math courses. The two main kinds of reasoning you use in life are inductive and deductive reasoning. Did you know that you have used inductive reasoning since you were a baby? It is the process of observing data, recognizing patterns, and making generalizations about those patterns. You learned correct ways of speaking by listening to the patterns of correct speech. Deductive reasoning is the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts. Lawyers use deductive reasoning to show how evidence proves their case based on the jury believing the evidence and accepting that is true. You will formulate models to represent problems and use both inductive and deductive reasoning.

## Part One: Recognizing Patterns

There is not a job out there today that can be accomplished without knowledge of how patterns work. For example, as a teacher, it is very important that I recognize patterns of how kids learn and what methods of instruction work best for different concepts.

In Geometry, we focus on VISUAL patterns and NUMBER patterns.

In Geometry, we focus on VISUAL patterns and NUMBER patterns.

## Part Two: Angle Relationships

Students must be able to understand the relationships between angles. These relationships include linear pairs, vertical angles, triangle and quadrilateral angles, perpendicular lines, same side interior angles, corresponding angles, alternate interior angles, alternate exterior angles and the angles of polygons.