Geometry Connections Book Cover

## Geometry Connections

### TEACHER RESOURCES

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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

 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 10.4 10.4 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

### 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...

### ETOOLS/VIDEOS

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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