(A Review and a Test conclude each chapter.)
1. Foundations of Geometry.
Logical Systems.
Points, Lines, and Planes.
Segments, Rays, and Angles.
2. Introduction to Proof.
Direct Proofs.
Proofs Involving Lines and Angles.
Constructions Involving Lines and Angles.
3. Triangles.
Classifying Triangles.
Congruent Triangles.
Proofs Involving Congruence.
Isosceles Triangles, Medians, and Altitudes.
Constructions Involving Triangles.
4. Parallel Lines and Polygons.
Indirect Proof and the Parallel Postulate.
Transversals and Angles.
Polygons and Angles.
Parallelograms and Rhombuses.
Rectangles, Squares, and Trapezoids.
Areas of Polygons.
5. Ratio, Proportion, and Similarity.
Ratio and Proportion.
Similar Polygons.
More Theorems on Similar Triangles.
6. Right Triangles and the Pythagorean Theorem.
Review of Radicals and Quadratic Equations (Optional).
Properties of Right Triangles.
The Pythagorean Theorem.
7. Circles.
Circles and Arcs.
Chords and Secants.
Tangents.
Circles and Regular Polygons.
Sectors, Arc Length, and Area.
8. Inequalities.
Inequalities.
Involving Triangles.
Inequalities Involving Circles.
9. Solid Geometry.
Planes and the Polyhedron.
Prisms and Pyramids.
Cylinders and Cones.
Spheres and Composite Features.
10. Geometric Loci.
Locus and Basic Theorems.
Triangle Concurrency Theorems.
11. Introduction to Analytic Geometry.
The Cartesian Coordinate System.
Slope, Distance, and Midpoint Formulas.
Circles.
Proofs Involving Polygons.
12. Triangle Trigonometry.
The Trigonometric Ratios.
Solving Right Triangles.
Applications Involving Right Triangles.
Appendixes.
Postulates of Geometry.
Theorems and Corollaries of Geometry.
Constructions in Geometry.
