# Chapter 7: Using Real Numbers and Right Triangles

## Introduction

In Math 8, the learning content is divided into Concepts. Each Concept is whole and complete providing focused learning on an indicated objective. Real-world Concepts involve the student in the learning objective of each Concept. Students are given opportunities to practice skills through real-world situations, examples, guided practice and independent practice sections. There are video links provided for Concept connections with technology. In this Chapter, students will engage with content that is related to using real numbers and right triangles. Concepts will include evaluating radical expressions, evaluating fractional powers, solving equations with radicals, classifying and comparing real numbers, irrational numbers, the Pythagorean Theorem, the Converse of the Pythagorean Theorem, indirect measurement, perimeter, area, the distance formula, special right triangles and trigonometric ratios.

## Chapter Outline

- 7.1. Evaluate Radical Expressions
- 7.2. Evaluate Radical Expressions and Fractional Powers
- 7.3. Solve Equations Involving Radicals
- 7.4. Classify Real Numbers
- 7.5. Approximate Solutions to Equations Involving Irrational Numbers
- 7.6. Derive and Use the Pythagorean Theorem
- 7.7. Derive and Use the Converse of the Pythagorean Theorem
- 7.8. Use the Pythagorean Theorem
- 7.9. The Pythagorean Theorem, Perimeter and Area
- 7.10. Identify and Use the Distance Formula
- 7.11. 45-45-90 Triangles
- 7.12. 30-60-90 Triangles
- 7.13. Understanding Sines
- 7.14. Understanding Cosines
- 7.15. Understanding Tangents
- 7.16. Determine and Use the Sine Ratio
- 7.17. Determine and Use the Cosine Ratio
- 7.18. Determine and Use the Tangent Ratio

### Chapter Summary

## Summary

Having completed this chapter, students are now ready to move on to the next Chapter. Each Concept has provided students with an opportunity to engage and practice skills in many Concepts including evaluating radical expressions, evaluating fractional powers, solving equations with radicals, classifying and comparing real numbers, irrational numbers, the Pythagorean Theorem, the Converse of the Pythagorean Theorem, indirect measurement, perimeter, area, the distance formula, special right triangles and trigonometric ratios.