Geometry – Full Course

True to traditional Geometry courses, topics include definitions, postulates, theorems, two-column proofs (mostly involving parallel lines and triangles), quadrilaterals, other polygons, circles, basic constructions, perimeter, area, solids, volume, surface area, analytic geometry and the basic trigonometric ratios. Geometry is taken either between or after the algebras in the sequence of courses. [There is no particular advantage either way.]

Table of Contents

Chapter 1 – LINE AND ANGLE RELATIONSHIPS

1.1 Sets, Statements and Reasoning
1.2 Informal Geometry and Measurement
1.3 Early Definitions and Postulates
1.4 Angles and Their Relationships
1.5 Introduction to Geometric Proof
1.6 Relationships: Perpendicular Lines
1.7 The Formal Proof of a Theorem

Chapter 2 – PARALLEL LINES

2.1 The Parallel Postulate and Special Angles
2.2 Indirect Proof
2.3 Proving Lines Parallel
2.4 The Angles of a Triangle
2.5 Convex Polygons
2.6 Symmetry and Transformations

Chapter 3 – TRIANGLES

3.1 Congruent Triangles
3.2 Corresponding Parts of Congruent Triangles
3.3 Isosceles Triangles
3.4 Basic Constructions Justified
3.5 Inequalities in a Triangle

Chapter 4 – QUADRILATERALS

4.1 Properties of a Parallelogram
4.2 The Parallelogram and Kite
4.3 The Rectangle, Square, and Rhombus
4.4 The Trapezoid

Chapter 5 – SIMILAR TRIANGLES

5.1 Ratios, Rates, and Proportions
5.2 Similar Polygons
5.3 Proving Triangles Similar
5.4 The Pythagorean Theorem
5.5 Special Right Triangles
5.6 Segments Divided Proportionately

Chapter 6 – CIRCLES

6.1 Circles and Related Segments and Angles
6.2 More Angle Measures in the Circle
6.3 Line and Segment Relationships in the Circle
6.4 Some Constructions and Inequalities for the Circle

Chapter 7 – LOCUS AND CONCURRENCE

7.1 Locus of Points
7.2 Concurrence of Lines
7.3 More About Regular Polygons

Chapter 8 – AREAS OF POLYGONS AND CIRCLES

8.1 Area and Initial Postulates
8.2 Perimeter and Area of Polygons
8.3 Regular Polygons and Area
8.4 Circumference and Area of a Circle
8.5 More Area Relationships in the Circle

Chapter 9 – SURFACES AND SOLIDS

9.1 Prisms, Area, and Volume
9.2 Pyramids, Area, and Volume
9.3 Cylinders and Cones
9.4 Polyhedrons and Spheres

Chapter 10 – ANALYTIC GEOMETRY

10.1 The Rectangular Coordinate System
10.2 Graphs of Linear Equations and Slope
10.3 Preparing to do Analytic Proofs
10.4 Analytic Proofs
10.5 Equations of Lines

Chapter 11 – INTRODUCTION TO TRIGONOMETRY

11.1 The Sine Ratio and Applications
11.2 The Cosine Ratio and Applications
11.3 The Tangent Ratio and Other Ratios
11.4 Applications with Acute Triangles

Sample Videos from this Course