CHAPTER 1 Lines, Angles, and Triangles
1.1 Historical Background of Geometry
1.2 Undefined Terms of Geometry: Point, Line, and Plane
2.1 Proof By Deductive Reasoning
2.4 Determining the Hypothesis and Conclusion
3.2 Isosceles and Equilateral Triangles
CHAPTER 4 Parallel Lines, Distances, and Angle Sums
4.3 Sum of the Measures of the Angles of a Triangle
4.4 Sum of the Measures of the Angles of a Polygon
4.5 Two New Congruency Theorems
CHAPTER 5 Parallelograms, Trapezoids, Medians, and Midpoints
5.3 Special Parallelograms: Rectangle, Rhombus, and Square
5.4 Three or More Parallels; Medians and Midpoints
6.1 The Circle; Circle Relationships
6.3 Measurement of Angles and Arcs in a Circle
7.8 Mean Proportionals in a Right Triangle
8.2 Angles of Elevation and Depression
9.1 Area of a Rectangle and of a Square
9.6 Polygons of the Same Size or Shape
9.7 Comparing Areas of Similar Polygons
CHAPTER 10 Regular Polygons and the Circle
10.2 Relationships of Segments in Regular Polygons of 3, 4, and 6 Sides
10.3 Area of a Regular Polygon
10.4 Ratios of Segments and Areas of Regular Polygons
10.5 Circumference and Area of a Circle
10.6 Length of an Arc; Area of a Sector and a Segment
10.7 Areas of Combination Figures
11.2 Locating Points by Means of Intersecting Loci
12.3 Distance Between Two Points
12.5 Locus in Analytic Geometry
12.6 Areas in Analytic Geometry
12.7 Proving Theorems with Analytic Geometry
CHAPTER 13 Inequalities and Indirect Reasoning
CHAPTER 14 Improvement of Reasoning
14.2 Deductive Reasoning in Geometry
14.3 Converse, Inverse, and Contrapositive of a Statement
14.4 Partial Converse and Partial Inverse of a Theorem
14.5 Necessary and Sufficient Conditions
15.2 Duplicating Segments and Angles
15.3 Constructing Bisectors and Perpendiculars
15.5 Constructing Parallel Lines
15.7 Inscribing and Circumscribing Regular Polygons
15.8 Constructing Similar Triangles
CHAPTER 16 Proofs of Important Theorems
CHAPTER 17 Extending Plane Geometry into Solid Geometry
17.2 Extensions to Solid Geometry
17.3 Areas of Solids: Square Measure
17.4 Volumes of Solids: Cubic Measure
18.1 Introduction to Transformations
CHAPTER 19 Non-Euclidean Geometry
19.1 The Foundations of Geometry
19.2 The Postulates of Euclidean Geometry
19.3 The Fifth Postulate Problem