**Table of Contents:**About the Author

Why Use This Book

Teaching Suggestions

Student Introduction

Glossary

Answers

**Chapter 1 - Fundamentals of Geometry Reasoning**Introduction to the Student

Geometry Notation

Geometry Notation Practice

All About Lines

All About Planes

Build It!

Three Planes in Space

**Chapter 2 - Uncovering All the Angles**Types of Angles

Complete the Chart

Triangle Activity

Triangle Practice

Quadrilateral Activity

Complementary and Supplementary Angles

Vertical Angles

Puzzle 1

Puzzle 2

Parallel Lines and Transversals I

Parallel Lines and Transversals II

Puzzle 3 - Find 20 Angles

**Chapter 3 - Triangle Properties**Triangle Properties 1: Sum of Angle Measures

Triangle Properties 2: Exterior Angle Property

Triangle Property 3: Sum of Two Sides

Triangle Properties Practice

Triangle Property 4: Largest Angle Faces Largest Side

Property of Equilateral and Isosceles Triangles

Algebra and Geometry Practice

**Chapter 4 - The Pythagorean Theorem**Exploration - What is a Theorem?

Pythagorean Triples

Practice with the Pythagorean Triples

Using the Pythagorean Theorem

Using the Pythagorean Applications

Problem Solving Strategies

Special Right Triangles

Chapter 5 - Uncovering All PolygonsPolygons – Investigation of Angles and Sides

Polygon Angles Exploration

Summary of Polygon Properties

Diagonals of a Polygon Exploration

The Number of Diagonals of a Polygon (Handshake Problem)

**Chapter 6 - Quadrilateral and Parallelogram Properties**The Quadrilateral Family

Venn Diagram Activity

Parallelogram Discovery

Parallelogram Properties

Working With Parallelograms

Experimenting With Parallelograms

A Look at Trapezoids

Kite! Kite! Kite!

Critical Thinking About Quadrilaterals

Median Investigation

Using Algebra to Solve Quadrilateral Problems

Quadrilateral Matching

**Chapter 7 - Metric Geometry**Perimeter and Circumference

Pi (ð) Investigation

Archimedes’ Idea for Approximating Pi

Area of Parallelograms

Parallelogram Area Activity

Area of Triangles and Trapezoids

Discovering the Area of a Trapezoid/ Area of a Trapezoid

Area of Circles

The Arbelos Problem

**Chapter 8 - Geometric Constructions**A Geometric Construction

How to Bisect an Angle

How to Copy an Angle

How to Construct a Perpendicular Bisector to a Line

Finding the Median in a Triangle

Area of Triangles and Trapezoids

Geometric Construction Review

Problem Solving With Geometric Constructions

Impossible Constructions?

**Chapter 9 - Geometry of Three Dimensional Shapes**3D Shapes - Prisms

The Volume of Cylinders

Volumes of Pyramids and Cones

Turn Up the Volume!

Volume of a Sphere

Surface Area of Prisms

Surface Area of a Cylinder Activity

Finding Surface Area of Prisms and Cylinders

Euler’s Formula

**Chapter 10 - Symmetry and Transformations**What is Vertical, Horizontal, and Point Symmetry?

Transformations - Reflections

Transformations - Translations

Transformations - Rotations

Transformations - Dilations

Glide Reflections and Compositions

Tessellations

**Chapter 11 - Proving Triangles Congruent**

Introduction to Proofs - Congruency

SSS Activity

SAS Activity

ASA and AAS Activities

SSA Activity

The Essence of a Good Geometric Proof

Picture, Statement, and Reason

Finding Congruent Triangles

Two Column Proofs

Investigate Hypotenuse - Leg Theorem

Similar Figures and Introduction to Similarity Proofs

Proving Triangles Similar

Test Your Reasoning Skills

**Chapter 12 - Coordinate Geometry**What is the Slope of a Line

Slope Formula

How to Write an Equation of a Line

The Midpoint Formula

The Distance Formula

Review Your Formulas

Introduction to Coordinate Proofs

**Reviews:**"As a teacher I like the problem solving activities as these could be used over again or with several students in the classroom." -iParenting Reviewer

"Mathematical Reasoning presents math in a way that makes it not only simple to learn, but also practical to apply to everyday circumstance (obviously making math more meaningful to him)." -Katherine, Mississippi

"My son hated math. I saw your curriculum and gave it a try. Wow, what a great fit for my son! Your Mathematical Reasoning curriculum gave him a way to learn math that made sense to him. Thank you!" -Amy, Ontario, Canada

"For the money, the books are excellent buys and worthy supplements to any childhood students education." -Maxine, "Teaching Children Mathematics" published by NCTM

"As a math instructor, I am so happy that it looks like I may have a math-brain in my family after all! He asks to do his math school work (Mathematical Reasoning book) every day!" -Janelle, Math Teacher & Parent

**Awards** (earned by various titles in series):

- Dr. Toy Best Picks
- Mensa Recommended Materials for the Gifted
- iParenting Media AwardMom's Choice Awards Silver Medal for Excellence
- iParenting Media Best Products
- Creative Child Magazine Preferred Choice AwardiParenting Media Excellent Products
- Cathy Duffy Top 100 Award
- Dr. Toy Product of Excellence
- Learning® Magazine Recommended Resource for Successful Teaching
- Jenkins Group Moonbeam Children's Book Award, Silver Medal
- Mom’s Choice Awards Gold Recipient