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 and Special Quadrilaterals Exercises p.64
1.6 Circles Exercises p.70
1.7 A Picture is Worth a Thousand Words Exercises p.76
1.8 Space Geometry Exercises p.83
Chapter 1 Review p.88

Chapter 2

Reasoning In Geometry

2.1 Inductive Reasoning Exercises p.96
2.2 Deductive Reasoning Exercises p.103
2.3 Finding the nth Term Exercises p.109
2.4 Mathematical Modeling Exercises p.115
2.5 Angle Relationships Exercises p.122
2.6 Special Angles on Parallel Lines Exercises p.129
Using Your Algebra Skills 2: Slope p.134
Chapter 2 Review p.138

Chapter 3

Using Tools Of Geometry

3.1 Duplicating Segments and Angles Exercises p.145
3.2 Constructing Perpendicular Bisectors Exercises p.149
3.3 Constructing Perpendiculars to a Line Exercises p.154
3.4 Constructing Angle Bisectors Exercises p.158
3.5 Constructing Parallel Lines Exercises p.162
Using Your Algebra Skills 3: Slopes of Parallel and Perpendicular Lines p.167
3.6 Construction Problems Exercises p.169
3.7 Constructing Points of Concurrency Exercises p.179
3.8 The Centroid Exercises p.186
Chapter 3 Review p.191

Chapter 4

Discovering And Proving Triangle Properties

4.1 Triangle Sum Conjecture Exercises p.201
4.2 Properties of Special Triangles Exercises p.206
Using Your Algebra Skills 4: Writing Linear Equations p.212
4.3 Triangle Inequalities Exercises p.216
4.4 Are There Congruence Shortcuts? Exercises p.222
4.5 Are There Other Congruence Shortcuts? Exercises p.227
4.6 Corresponding Parts of Congruent Triangles Exercises p.231
4.7 Flowchart Thinking Exercises p.237
4.8 Proving Isosceles Triangle Conjectures Exercises p.243
Chapter 4 Review p.249

Chapter 5

Discovering And Proving Polygon Properties

5.1 Polygon Sum Conjecture Exercises p.257
Improving Your Visual Thinking Skills p.259
5.2 Exterior Angles of a Polygon Exercises p.262
5.3 Kite and Trapezoid Properties Exercises p.269
5.4 Properties of Midsegments Exercises p.275
5.5 Properties of Parallelograms Exercises p.281
Using Your Algebra Skills 5: Solving Systems of Linear Equations p.286
5.6 Properties of Special Parallelograms Exercises p.290
5.7 Proving Quadrilateral Properties Exercises p.296
Chapter 5 Review p.300

Chapter 6

Discovering And Proving Circle Properties

6.1 Chord Properties Exercises p.310
6.2 Tangent Properties Exercises p.315
6.3 Arcs and Angles Exercises p.322
6.4 Proving Circle Conjectures Exercises p.327
Using Your Algebra Skills 6: Finding the Circumcenter p.330
6.5 The Circumference/Diameter Ratio Exercises p.333
6.6 Around the World Exercises p.338
6.7 Arc Length Exercises p.343
Chapter 6 Review p.349

Chapter 7

Transformations And Tessellations

7.1 Transformations and Symmetry Exercises p.362
7.2 Properties of Isometries Exercises p.370
7.3 Compositions of Transformations Exercises p.376
7.4 Tessellations with Regular Polygons Exercises p.382
7.5 Tessellations with Nonregular Polygons Exercises p.386
7.6 Tessellations Using Only Translations Exercises p.390
7.7 Tessellations That Use Rotations Exercises p.395
7.8 Tessellations That Use Glide Reflections Exercises p.399
Using Your Algebra Skills 7: Finding the Orthocenter and Centroid p.403
Chapter 7 Review p.404

Chapter 8


8.1 Areas of Rectangles and Parallelograms Exercises p.413
8.2 Areas of Triangles, Trapezoids, and Kites Exercises p.418
8.3 Area Problems Exercises p.423
8.4 Areas of Regular Polygons Exercises p.427
8.5 Areas of Circles Exercises p.435
8.6 Any Way You Slice It Exercises p.439
8.7 Surface Area Exercises p.450
Chapter 8 Review p.455

Chapter 9

The Pythagorean Theorem

9.1 The Theorem of Pythagoras Exercises p.465
9.2 The Converse of the Pythagorean Theorem Exercises p.470
Using Your Algebra Skills 8: Radical Expressions p.474
9.3 Two Special Right Triangles Exercises p.477
9.4 Story Probelms Exercises p.482
9.5 Distance in Coordinate Geometry Exercises p.489
9.6 Circles and the Pythagorean Theorem Exercises p.493
Chapter 9 Review p.496

Chapter 10


10.1 The Geometry of Solids Exercises p.508
10.2 Volume of Prisms and Cylinders Exercises p.517
10.3 Volume of Pyramids and Cones Exercises p.524
10.4 Volume Problems Exercises p.532
10.5 Displacement and Density Exercises p.536
10.6 Volume of a Sphere Exercises p.543
10.7 Surface Area of a Sphere Exercises p.547
Chapter 10 Review p.554

Chapter 11


Using Your Algebra Skills 9: Proportion and Reasoning p.561
11.1 Similar Polygons Exercises p.568
11.2 Similar Triangles Exercises p.574
11.3 Indirect Measurement with Similar Triangles Exercises p.582
11.4 Corresponding Parts of Similar Triangles Exercises p.588
11.5 Proportions with Area and Volume Exercises p.595
11.6 Proportional Segments Between Parallel Lines Exercises p.607
Chapter 11 Review p.614

Chapter 12


12.1 Trigonometric Ratios Exercises p.624
12.2 Problem Solving with Right Triangles Exercises p.628
12.3 The Law of Sines Exercises p.637
12.4 The Law of Cosines Exercises p.643
12.5 Problem Solving with Trigonometry Exercises p.648
Chapter 12 Review p.659

Chapter 13

Geometry As A Mathematical System

13.1 The Premises of Geometry Exercises p.674
13.2 Planning a Geometry Proof Exercises p.684
13.3 Triangle Proofs Exercises p.688
13.4 Quadrilateral Proofs Exercises p.693
13.5 Indirect Proof Exercises p.700
13.6 Circle Proofs Exercises p.704
13.7 Similarity Proofs Exercises p.709
Using Your Algebra Skills 10: Coordinate Proof p.716
Chapter 13 Review p.721
Discovering Geometry: An Investigative Approach, 3rd Edition



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