Chapter 0

Geometric Art

0.1 Geometry in Nature and in Art Exercises p.4
Improving Your Visual Thinking Skills p.6
0.2 Line Designs Exercises p.8
Improving Your Algebra Skills p.9
0.3 Circle Designs Exercises p.12
0.4 Op Art Exercises p.15
0.5 Knot Designs Exercises p.18
0.6 Islamic Tile Designs Exercises p.22
Chapter 0 Review p.24

Chapter 1

Introducing Geometry

1.1 Building Blocks of Geometry Exercises p.33
Using Your Algebra Skills 1: Midpoint p.37
1.2 Poolroom Math Exercises p.42
1.3 What's a Widget Exercises p.51
1.4 Polygons Exercises p.56
1.5 Triangles Exercises p.62
1.6 Special Quadrilaterals Exercises p.66
1.7 Circles Exercises p.72
1.8 Space Geometry Exercises p.78
1.9 A Picture Is Worth a Thousand Words Exercises p.84
Chapter 1 Review p.90

Chapter 2

Reasoning In Geometry

2.1 Inductive Reasoning Exercises p.98
2.2 Finding the nth Term Exercises p.105
2.3 Mathematical Modeling Exercises p.112
2.4 Deductive Reasoning Exercises p.117
2.5 Angle Relationships Exercises p.124
2.6 Special Angles on Parallel Lines Exercises p.131
Using Your Algebra Skills 2: Slope p.136
Chapter 2 Review p.139

Chapter 3

Using Tools Of Geometry

3.1 Duplicating Segments and Angles Exercises p.147
3.2 Constructing Perpendicular Bisectors Exercises p.151
3.3 Constructing Perpendiculars to a Line Exercises p.156
3.4 Constructing Angle Bisectors Exercises p.160
3.5 Constructing Parallel Lines Exercises p.164
Using Your Algebra Skills 3: Slopes of Parallel and Perpendicular Lines p.169
3.6 Construction Problems Exercises p.171
3.7 Constructing Points of Concurrency Exercises p.181
3.8 The Centroid Exercises p.188
Chapter 3 Review p.193

Chapter 4

Discovering And Proving Triangle Properties

4.1 Triangle Sum Conjecture Exercises p.203
4.2 Properties of Isosceles Triangles Exercises p.208
Using Your Algebra Skills 4: Solving Equations p.214
4.3 Triangle Inequalities Exercises p.218
4.4 Are There Congruence Shortcuts? Exercises p.224
4.5 Are There Other Congruence Shortcuts? Exercises p.229
4.6 Corresponding Parts of Congruent Triangles Exercises p.233
4.7 Flowchart Thinking Exercises p.239
4.8 Proving Special Triangle Conjectures Exercises p.245
Chapter 4 Review p.251

Chapter 5

Discovering And Proving Polygon Properties

5.1 Polygon Sum Conjecture Exercises p.259
5.2 Exterior Angles of a Polygon Exercises p.263
5.3 Kite and Trapezoid Properties Exercises p.271
5.4 Properties of Midsegments Exercises p.277
5.5 Properties of Parallelograms Exercises p.283
Using Your Algebra Skills 5: Writing Linear Equations p.289
5.6 Properties of Special Parallelograms Exercises p.294
5.7 Proving Quadrilateral Properties Exercises p.300
Chapter 5 Review p.304

Chapter 6

Discovering And Proving Circle Properties

6.1 Tangent Properties Exercises p.313
6.2 Chord Properties Exercises p.320
6.3 Arcs and Angles Exercises p.327
6.4 Proving Circle Conjectures Exercises p.332
6.5 The Circumference/Diameter Ratio Exercises p.337
6.6 Around the World Exercises p.342
Using Your Algebra Skills 6: Solving Systems of Linear Equations p.348
6.7 Arc Length Exercises p.351
Chapter 6 Review p.359

Chapter 7

Transformations And Tessellations

7.1 Transformations and Symmetry Exercises p.372
7.2 Properties of Isometries Exercises p.380
7.3 Compositions of Transformations Exercises p.386
7.4 Tessellations with Regular Polygons Exercises p.392
7.5 Tessellations with Nonregular Polygons Exercises p.396
7.6 Tessellations Using Only Translations Exercises p.400
7.7 Tessellations That Use Rotations Exercises p.405
7.8 Tessellations That Use Glide Reflections Exercises p.411
Using Your Algebra Skills 7: Finding Points of Concurrency p.415
Chapter 7 Review p.416

Chapter 8


8.1 Areas of Rectangles and Parallelograms Exercises p.425
8.2 Areas of Triangles, Trapezoids, and Kites Exercises p.430
8.3 Area Problems Exercises p.435
Using Your Algebra Skills 8: Products, Factors, and Quadratic Functions p.440
8.4 Areas of Regular Polygons Exercises p.443
8.5 Areas of Circles Exercises p.451
8.6 Any Way You Slice It Exercises p.455
8.7 Surface Area Exercises p.466
Chapter 8 Review p.471

Chapter 9

The Pythagorean Theorem

9.1 The Theorem of Pythagoras Exercises p.481
9.2 The Converse of the Pythagorean Theorem Exercises p.486
Using Your Algebra Skills 9: Radical Expressions p.490
9.3 Two Special Right Triangles Exercises p.493
9.4 Story Problems Exercises p.498
9.5 Distance in Coordinate Geometry Exercises p.504
9.6 Circles and the Pythagorean Theorem Exercises p.509
Chapter 9 Review p.512

Chapter 10


10.1 The Geometry of Solids Exercises p.524
10.2 Volume of Prisms and Cylinders Exercises p.533
10.3 Volume of Pyramids and Cones Exercises p.540
10.4 Volume Problems Exercises p.548
10.5 Displacement and Density Exercises p.552
10.6 Volume of a Sphere Exercises p.559
10.7 Surface Area of Sphere Exercises p.563
Using Your Algebra Skills 10: Solving for Any Variable p.568
Chapter 10 Review p.572

Chapter 11


Using Your Algebra Skills 11: Proportion and Reasoning p.579
11.1 Similar Polygons Exercises p.585
11.2 Similar Triangles Exercises p.591
11.3 Indirect Measurement with Similar Triangles Exercises p.599
11.4 Corresponding Parts of Similar Triangles Exercises p.605
11.5 Proportions with Area Exercises p.610
11.6 Proportions with Volume Exercises p.616
11.7 Proportional Segments Between Parallel Lines Exercises p.627
Chapter 11 Review p.634

Chapter 12


12.1 Trigonometric Ratios Exercises p.644
12.2 Problem Solving with Right Triangles Exercises p.648
12.3 The Law of Sines Exercises p.657
12.4 The Law of Cosines Exercises p.663
12.5 Problem Solving with Trigonometry Exercises p.668
Using Your Algebra Skills 12: Transformation Functions p.677
Chapter 12 Review p.683

Chapter 13

Geometry As A Mathematical System

13.1 The Premises of Geometry Exercises p.698
13.2 Planning a Geometry Proof Exercises p.708
13.3 Triangle Proofs Exercises p.712
13.4 Quadrilateral Proofs Exercises p.717
13.5 Indirect Proof Exercises p.724
13.6 Circle Proofs Exercises p.728
13.7 Similarity Proofs Exercises p.733
Using Your Algebra Skills 13: Coordinate Proof p.741
Chapter 13 Review p.745
Discovering Geometry: An Investigative Approach



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