Mathematics 101 - Geometry Study Guide | Complete Practice Problems & Solutions | Geometry Exam Prep

Geometry
Course: Mathematics 101 - Geometry




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GEOMETRY
Course Overview

This 40-page guide provides comprehensive coverage of Geometry following a
structured academic format. Each section includes clear explanations, theorems,
proofs, formulas, and practical applications.




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TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION TO GEOMETRY (Pages 4-8)

1.1 Basic Geometric Concepts
1.2 Points, Lines, and Planes
1.3 Angles and Their Properties
1.4 Postulates and Theorems
1.5 Geometric Proofs


CHAPTER 2: TRIANGLES (Pages 9-15)

2.1 Types of Triangles
2.2 Triangle Properties and Theorems
2.3 Congruent Triangles


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,2.4 Similar Triangles
2.5 Pythagorean Theorem
2.6 Triangle Inequalities


CHAPTER 3: QUADRILATERALS (Pages 16-20)

3.1 Types of Quadrilaterals
3.2 Properties of Parallelograms
3.3 Special Parallelograms
3.4 Trapezoids and Kites
3.5 Area and Perimeter Formulas


CHAPTER 4: CIRCLES (Pages 21-26)

4.1 Circle Terminology
4.2 Circle Theorems
4.3 Arcs and Chords
4.4 Tangents and Secants
4.5 Circumference and Area


CHAPTER 5: COORDINATE GEOMETRY (Pages 27-31)

5.1 Coordinate System Basics
5.2 Distance and Midpoint Formulas
5.3 Slope and Equations of Lines
5.4 Parallel and Perpendicular Lines
5.5 Geometric Transformations


CHAPTER 6: SOLID GEOMETRY (Pages 32-36)

6.1 Three-Dimensional Figures
6.2 Volume Formulas
6.3 Surface Area Formulas
6.4 Cross-Sections and Projections


CHAPTER 7: TRIGONOMETRY IN GEOMETRY (Pages 37-40)

7.1 Right Triangle Trigonometry
7.2 Law of Sines
7.3 Law of Cosines
7.4 Applications and Problem Solving



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, APPENDICES

Appendix A: Formula Sheet
Appendix B: Theorem Reference
Appendix C: Practice Problems
Appendix D: Glossary of Terms




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TABLE OF CONTENTS (Continued)

Detailed Chapter Breakdown

CHAPTER 1: INTRODUCTION TO GEOMETRY (4 pages)

 Undefined terms: point, line, plane
 Defined terms: segment, ray, angle
 Angle classifications and measurements
 Basic postulates and theorems
 Introduction to geometric proofs

CHAPTER 2: TRIANGLES (6 pages)

 Classification by sides and angles
 Angle sum theorem
 Triangle congruence (SSS, SAS, ASA, AAS, HL)
 Triangle similarity (AA, SSS, SAS)
 Pythagorean theorem and applications
 Triangle inequality theorems

CHAPTER 3: QUADRILATERALS (5 pages)

 Classification hierarchy
 Properties of quadrilaterals
 Parallelogram theorems
 Special quadrilaterals: rectangle, rhombus, square
 Area formulas and derivations

CHAPTER 4: CIRCLES (5 pages)




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,  Circle vocabulary
 Central angles and arcs
 Chord theorems
 Tangent theorems
 Inscribed angles
 Circumference and area formulas

CHAPTER 5: COORDINATE GEOMETRY (5 pages)

 Cartesian coordinate system
 Distance formula derivation
 Midpoint formula
 Slope and line equations
 Transformations: translation, rotation, reflection

CHAPTER 6: SOLID GEOMETRY (5 pages)

 Prisms, pyramids, cylinders, cones, spheres
 Volume formula derivations
 Surface area calculations
 Cross-sections and Euler's formula

CHAPTER 7: TRIGONOMETRY (4 pages)

 Trigonometric ratios
 Special right triangles
 Law of sines and cosines
 Applications in geometry

APPENDICES (6 pages)

 Complete formula reference
 Theorem summary
 Practice problems with solutions
 Glossary of geometric terms




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