Geometry Connections Book Cover

Geometry Connections Book Cover

Geometry Connections

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TABLE OF CONTENTS

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Chapter 1: Problem Solving
Opening 1.OP Chapter Opening
Section 1.1 1.1.1 Creating a Quilt Using Symmetry
1.1.2 Making Predictions and Investigating Results
1.1.3 Perimeter and Area of Enlarging Tile Patterns
1.1.4 Logical Arguments
1.1.5 Building a Kaleidoscope
Section 1.2 1.2.1 Spatial Visualization and Reflections
1.2.2 Rigid Transformations: Rotations and Translations
1.2.3 Using Transformations
1.2.4 Using Transformations to Create Shapes
1.2.5 Symmetry
Section 1.3 1.3.1 Attributes and Characteristics of Shapes
1.3.2 More Characteristics of Shapes
1.3.3 Introduction to Probability
Closure 1.CL Chapter Closure

Chapter 2: Angles and Measurement
Opening 2.OP Chapter Opening
Section 2.1 2.1.1 Complementary, Supplementary, and Vertical Angles
2.1.2 Angles Formed by Transversals
2.1.3 More Angles Formed by Transversals
2.1.4 Angles in a Triangle
2.1.5 Applying Angle Relationships
Section 2.2 2.2.1 Units of Measure
2.2.2 Areas of Triangles and Composite Shapes
2.2.3 Areas of Parallelograms and Trapezoids
2.2.4 Heights and Area
Section 2.3 2.3.1 Squares and Square Roots
2.3.2 Triangle Inequality
2.3.3 The Pythagorean Theorem
Closure 2.CL Chapter Closure

Chapter 3: Justification and Similarity
Opening 3.OP Chapter Opening
Section 3.1 3.1.1 Similarity
3.1.2 Proportional Growth and Ratios
3.1.3 Using Ratios of Similarity
3.1.4 Applications and Notation
Section 3.2 3.2.1 Conditions for Triangle Similarity
3.2.2 Creating a Flowchart
3.2.3 Triangle Similarity and Congruence
3.2.4 More Conditions for Triangle Similarity
3.2.5 Determining Similarity
3.2.6 Applying Similarity
Closure 3.CL Chapter Closure

Chapter 4: Trigonometry and Probability
Opening 4.OP Chapter Opening
Section 4.1 4.1.1 Constant Ratios in Right Triangles
4.1.2 Connecting Slope Ratios to Specific Angles
4.1.3 Expanding the Trig Table
4.1.4 The Tangent Ratio
4.1.5 Applying the Tangent Ratio
Section 4.2 4.2.1 Introduction to Probability Models
4.2.2 Theoretical and Experimental Probability
4.2.3 Using an Area Model
4.2.4 Choosing a Probability Model
4.2.5 Optional: Applications of Probability Methods
Closure 4.CL Chapter Closure

Chapter 5: Completing the Triangle Toolkit
Opening 5.OP Chapter Opening
Section 5.1 5.1.1 Sine and Cosine Ratios
5.1.2 Selecting a Trig Tool
5.1.3 Inverse Trigonometry
5.1.4 Trigonometric Applications
Section 5.2 5.2.1 Special Right Triangles
5.2.2 Pythagorean Triples
Section 5.3 5.3.1 Finding Missing Parts of Triangles
5.3.2 Law of Sines
5.3.3 Law of Cosines
5.3.4 Ambiguous Triangles
5.3.5 Choosing a Tool
Closure 5.CL Chapter Closure

Chapter 6: Congruent Triangles
Opening 6.OP Chapter Opening
Section 6.1 6.1.1 Congruent Triangles
6.1.2 Conditions for Triangle Congruence
6.1.3 Flowcharts for Congruence
6.1.4 Converses
Section 6.2 6.2.1 Angles on a Pool Table
6.2.2 Investigating a Triangle
6.2.3 Creating a Mathematical Model
6.2.4 Analyzing a Game
6.2.5 Using Transformations and Symmetry to Create a Snowflake
Closure 6.CL Chapter Closure

Chapter 7: Proof and Quadrilaterals
Opening 7.OP Chapter Opening
Section 7.1 7.1.1 Properties of a Circle
7.1.2 Building a Tetrahedron
7.1.3 Shortest Distance Problems
7.1.4 Using Symmetry to Study Polygons
Section 7.2 7.2.1 Special Quadrilaterals and Proof
7.2.2 Properties of Rhombi
7.2.3 More Proof with Congruent Triangles
7.2.4 More Properties of Quadrilaterals
7.2.5 Two-Column Proofs
7.2.6 Explore-Conjecture-Prove
Section 7.3 7.3.1 Studying Quadrilaterals on a Coordinate Grid
7.3.2 Coordinate Geometry and Midpoints
7.3.3 Quadrilaterals on a Coordinate Plane
Closure 7.CL Chapter Closure

Chapter 8: Polygons and Circles
Opening 8.OP Chapter Opening
Section 8.1 8.1.1 Pinwheels and Polygons
8.1.2 Interior Angles of a Polygon
8.1.3 Angles of Regular Polygons
8.1.4 Regular Polygon Angle Connections
8.1.5 Finding the Area of Regular Polygons
Section 8.2 8.2.1 Area Ratios of Similar Figures
8.2.2 Ratios of Similarity
Section 8.3 8.3.1 A Special Ratio
8.3.2 Area and Circumference of Circles
8.3.3 Circles in Context
Closure 8.CL Chapter Closure

Chapter 9: Solids and Constructions
Opening 9.OP Chapter Opening
Section 9.1 9.1.1 Three-Dimensional Solids
9.1.2 Volume and Surface Area of Prisms
9.1.3 Prisms and Cylinders
9.1.4 Volumes of Similar Solids
9.1.5 Ratios of Similarity
Section 9.2 9.2.1 Introduction to Construction
9.2.2 Constructing Bisectors
9.2.3 More Exploration with Constructions
9.2.4 Finding a Centroid
Closure 9.CL Chapter Closure

Chapter 10: Circles and Expected Value
Opening 10.OP Chapter Opening
Section 10.1 10.1.1 Introduction to Chords
10.1.2 Angles and Arcs
10.1.3 Chords and Angles
10.1.4 Tangents and Chords
10.1.5 Problem Solving with Circles
Section 10.2 10.2.1 Designing Spinners
10.2.2 Expected Value
10.2.3 More Expected Value
Section 10.3 10.3.1 The Equation of a Circle
Section 10.410.4 Laws of Exponents
Closure 10.CL Chapter Closure

Chapter 11: Solids and Circles
Opening 11.OP Chapter Opening
Section 11.1 11.1.1 Platonic Solids
11.1.2 Pyramids
11.1.3 Volume of a Pyramid
11.1.4 Surface Area and Volume of a Cone
11.1.5 Surface Area and Volume of a Sphere
Section 11.2 11.2.1 Coordinates on a Sphere
11.2.2 Tangents and Arcs
11.2.3 Secant and Tangent Relationships
Section 11.3 11.3.1 Relation Treasure Hunt
Closure 11.CL Chapter Closure

Chapter 12: Conics and Closure
Opening 12.OP Chapter Opening
Section 12.1 12.1.1 Introduction to Conic Sections
12.1.2 Graphing Parabolas Using the Focus and Directrix
12.1.3 Circles and Ellipses
12.1.4 The Hyperbola
12.1.5 Conic Equations and Graphs
Section 12.2 12.2.1 Using Coordinate Geometry and Construction to Explore Shapes
12.2.2 Euler’s Formula for Polyhedra
12.2.3 The Golden Ratio
12.2.4 Using Geometry to Find Probability
Closure 12.CL Chapter Closure

Appendices
A Points, Lines, and Planes
B Euclidean Geometry
C Non-Euclidean Geometry

Glossary
Index
 
 

RESOURCE PAGES

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Chapter 1: Problem Solving
Chapter 2: Angles and Measurement
Chapter 3: Justification and Similarity
Chapter 4: Trigonometry and Probability
Chapter 5: Completing the Triangle Toolkit
Chapter 6: Congruent Triangles
Chapter 7: Proof and Quadrilaterals
Chapter 8: Polygons and Circles
Chapter 9: Solids and Constructions
Chapter 10: Circles and Expected Value
Chapter 11: Solids and Circles
Chapter 12: Conics and Closure

PARENT GUIDE W/ EXTRA PRACTICE

Welcome to the Geometry Connections Parent Guide. The purpose of this guide is to assist you should your child need help with homework or the ideas in the course. We believe all students can be successful in mathematics as long as they are willing to work and ask for help when they need it. We encourage you to contact your child’s teacher if your student has additional questions that this guide or other resources do not answer.   Read More...


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General eTools
Chapter 1: Problem Solving
Chapter 2: Angles and Measurement
Chapter 3: Justification and Similarity
Chapter 4: Trigonometry and Probability
Chapter 5: Completing the Triangle Toolkit
Chapter 6: Congruent Triangles
Chapter 7: Proof and Quadrilaterals
Chapter 8: Polygons and Circles
Chapter 9: Solids and Constructions
Chapter 10: Circles and Expected Value
Chapter 11: Solids and Circles
Chapter 12: Conics and Closure

PÁGINA DE RECURSOS

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Capítulo 1
Capítulo 2
Capítulo 3
Capítulo 4
Capítulo 5
Capítulo 6
Capítulo 7
Capítulo 8
Capítulo 9
Capítulo 10
Capítulo 11
Capítulo 12

SUPPORT MATERIALS

GC: Geometry Connections: Quick Reference Guide PDF
GC: Geometry Connections: Course Overview PD
GC: Geometry Connections: Development of Major Content Strands PDF

If you have adopted the CPM curriculum and do not have a teacher edition, please contact our Business Office at (209) 745-2055  for information to obtain a copy.