# Ch 19: Proofs & Reasoning in Math

### About This Chapter

## Proofs & Reasoning in Math - Chapter Summary

This chapter breaks down different forms of mathematical proofs and reasoning, equipping you with helpful tools to navigate fundamental calculations and problem solving. You can expect to come out of this chapter with an improved comprehension of the following topics:

- Direct and indirect proofs
- Deductive and inductive reasoning
- Formal and informal reasoning
- Problem solving principles
- Using estimation to confirm calculated results

The printable practice quizzes attached to each lesson allow you to make sure you're processing the material step-by-step before continuing to another subject. And once you're through with the lessons, the practice final exam can help you determine your overall understanding of the chapter's content.

### 1. Direct Proofs: Definition and Applications

In mathematics, direct proof is a tool used to show if a conditional statement is true or false. Learn how to define a conditional statement and how to use applications of direct proof to determine if a conditional statement is true or false.

### 2. Indirect Proof in Geometry: Definition & Examples

There are many different methods that can be used to prove a given theory. One of those methods is indirect proof. In this lesson, we will explore indirect proof and learn the steps taken to use this method to prove a given theory.

### 3. Inductive & Deductive Reasoning in Geometry: Definition & Uses

In geometry, inductive reasoning is based on observations, while deductive reasoning is based on facts, and both are used by mathematicians to discover new proofs. Learn about the definition and uses of inductive and deductive reasoning in geometry, and discover that one type of reasoning is based on observations while the other is based on facts.

### 4. Mathematical Principles for Problem Solving

Solving problems, both in math and in life, involves five mathematical principles: always, counterexample, order, splitting hairs, and analogies. Delve into the definition of each principle and learn when and how to use them.

### 5. Verifying Calculated Results with Estimation

Estimation uses approximation to reach near-exact results with minimal calculation. Learn how to verify calculated results, and how to use estimation through a provided example.

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### Other Chapters

Other chapters within the TExES Mathematics/Science 4-8 (114): Practice & Study Guide course

- Number Concepts
- Number Operations & Problem Solving
- Number Theory & Applications
- Linear Functions & Inequalities
- Linear Models
- Nonlinear Functions
- Quadratic Equations
- Basic Calculus Concepts
- Measurement & the Metric System Overview
- Geometric Relationships
- Basic Geometric Figures
- 3D Figures & 2D Representations
- Transformational Geometry
- Tables and Plots for Data
- Data Summarization in Math
- Evaluating Probabilities
- Sampling & Statistical Interference
- Basic Mathematical Reasoning
- Applications of Mathematics
- Mathematical Instruction
- Student-Centered Math Instructional Strategies
- Mathematical Assessments
- Safety Procedures and Hazards in Scientific Research
- Analyzing and Interpreting Scientific Data
- Nature & Impact of Science
- Population Growth & Trends
- Natural Resources & Their Consumption
- Unifying Concepts & Processes in Science
- Systems in Science
- Scientific Models
- Basics of Force and Motion
- Mechanics
- Structure of Matter
- Periodic Table
- Chemical Bonds
- Chemical Formulas, Reactions & Equations
- Chemistry Applications
- Work, Power & Energy
- Heat & Electric Energy
- Magnetism
- Light, Sound & Waves
- Energy Transformations
- Classification of Organisms
- Structure & Function of Living Things
- Compounds & Molecules
- Reproduction & Heredity
- Evolution & Adaptations
- Regulatory Mechanisms & Behavior
- Organisms & the Environment
- Earth's Features
- Energy Sources & Heat Transfer in Earth Science
- Cycles in Earth Systems
- Humans & the Environment
- Climate & Weather
- Components of the Solar System & Universe
- Earth in the Solar System
- History & Formation of the Earth
- Science Instruction & Assessment
- TExES Mathematics/Science 4-8 Flashcards