# GEOMETRY ACADEMIC LIBRARY

*First Semester*

## Geometry Online First Semester

##### UNIT 1 – INTRODUCTION

- Course Overview
- Mathematics System: Set Theory Review
- Mathematics System: Operations with Sets
- Quiz 1: Set Theory
- Geometry Undefined Terms: Point
- Geometry Undefined Terms: Line
- Geometry Undefined Terms: Plane
- Quiz 2: Undefined Terms
- Defined Terms: Definitions
- Quiz 3: Defined Terms
- Geometric Postulates
- Language and Notation of Basic Geometry (The student will use concepts covered in this basic review of geometric terms throughout the course)
- Definitions, Postulates and Theorems

- Review of Algebraic Postulates
- Geometric Theorems
- Review of Properties of Algebra
- Quiz 4: Postulates and Theorems
- Test
- Alternate Test
- Glossary and Credits

##### UNIT 2 – LOGIC

- Logic
- Conjunctions
- Conjunctions, Disjunctions, and Negations
- Geometry – Conjunctions and Disjunctions
- Truth Table for Negation, Conjunctions, and Disjunctions (This instructional presentation is best viewed after becoming acquainted with the material in the three assignments. The video moves rapidly and is for a course in college, but clearly explains the concepts.)
- Introduction to Logic
- Mathematical Statements and Truth Value

- Disjunctions
- Negation
- Conditional or Implication Statements
- Converse, Inverse, Contrapositive
- Quiz 1: Principles of Logic
- Counterexamples
- Inductive Reasoning
- Deductive Reasoning
- Using Deductive Reasoning
- Quiz 2: Inductive and Deductive Reasoning
- Proof Formats: Statement of the Theorem (Use the instructional presentations in this section for all the assignments. Additional information for explanations may take you to different Internet sites and are intended for supplemental information as needed by the student. Please remember that some of these instructional presentations may be on You Tube and have advertising associated with them prior to the presentation. The Academy does not control that aspect and typically you may skip the ad before it plays completely)
- Proof Formats: The Figure
- Proof Formats: The Given Statement
- Proof Formats: To Prove Statement
- Proof Formats: The Plan of the Proof
- Indirect Proof Format: The Paragraph Proof
- Quiz 3: Proof Formats
- Test
- Alternate Test
- Glossary and Credits

##### UNIT 3 – ANGLES AND PARALLELS

- Angle Definitions
- Angle Measurement
- Quiz 1: Angles
- Geometric Proof
- Angle Relationship Definitions
- Angle Relationship Theorems (1)
- Angle Relationship Theorems (2)
- Quiz 2: Angle Theorems
- Construction: Copying Figures
- Construction: Bisecting Figures
- Basic Properties of Parallels
- Transversals and Special Angles
- More Proofs: Transversals and Special Angles (Students should use the previous instructional presentations for their work in this lesson)
- Continued Proofs: Transversals and Special Angles (Students should use the previous instructional presentations for their work in this lesson)
- More Proofs for Postulates 9 and 10– (Students should use the previous instructional presentations for their work in this lesson)
- Quiz 3: Parallels and Transversals
- Construction: Perpendiculars
- Construction: Tangents to Circles
- Construction: Parallels
- Classifying Triangles by Sides and Angles
- Exterior and Remote Interior Angles of a Triangle
- Proofs Involving Triangles
- Other Polygons
- Quiz 4: Triangles, Polygons, and Angle Properties
- Test
- Alternate Test
- Glossary and Credits

##### UNIT 4 – CONGRUENT TRIANGLES AND QUADRILATERALS

- Defining Congruent Triangles
- Proving Triangles Congruent (1)
- Proving Triangles Congruent (2)
- Proving Triangles Congruent (3)
- Proving Right Triangles Congruent
- Quiz 1: Congruent Triangles
- Independent Triangles (1)
- Independent Triangles (2)
- Overlapping Triangles (1)
- Overlapping Triangles (2)
- Isosceles Triangles (1)
- Isosceles Triangles (2)
- Construction of Triangles 30-60-90 (In this lesson you will practice construction techniques that you already know in order to construct triangles from different given information including 30-60-90 right triangles. Read the written instructions carefully, and study the diagrams. Then view the videos which show step-by-step the construction details. First, you will see how to construct triangles with specific parts. Sometimes the lengths of the sides will be given; sometimes an angle measure will also be stated. To think about constructing a triangle given its three sides, remember the triangle inequality theorem. It states that the sum of the two sides of a triangle is greater than the third side. This statement lets you know that the other two sides will intersect somewhere off the third side. Follow the directions given to you to complete this assignment. Follow the directions given to you to complete this assignment)
- Construction of Triangles 45-45-90
- Constructing Inscribed Shapes
- Quiz 2: Types of Triangles
- Inequality Theorem in One Triangle Part 1
- Triangle Inequality Theorem (This instructional presentation will present material that will be somewhat different in the place presented in your assignment, but will be helpful to you)
- Triangle Inequality Theorem
- Triangle Inequality Theorem

- Inequality Theorem in One Triangle Part 2 (Use the instructional presentations from the previous assignment as needed for this current lesson)
- Inequality Theorem in Two Triangles
- Quadrilateral Parallelograms Theorems Part 1
- Quadrilateral Parallelograms Theorems Part 2 (Use the instructional presentations from the previous assignment as needed for this current lesson)
- Quiz 3: Inequalities; Quadrilaterals
- Triangles that Use Parallelograms in Proofs (Review any of the instructional presentations in the previous section as needed for this lesson)
- Parallelograms: Rectangles
- Parallelograms: Rhombus
- Trapezoids-Definitions and Proofs
- Quiz 4: Parallelograms; Trapezoids
- Test
- Alternate Test
- Glossary and Credits

##### UNIT 5 – SIMILAR POLYGONS

- Algebra and Ratios
- Algebra Properties and Proportions
- Properties of Proportions
- Quiz 1: Ratios, Properties, and Proportions
- Meaning of Similarity
- Meaning of Similarity-Theorems
- Meaning of Similarity-Proofs
- Theorems-Similar Polygons
- Theorems-Special Segments in Triangles
- Similar Right Triangles
- The Pythagorean Theorem
- Theorem about 30-60-90 Right Triangles
- Theorem about 45-45-90 Right Triangles
- Quiz 2: Similarity; Triangle Theorems
- Using Triangles: Rectangular Solids
- Using Triangles: Regular Square Pyramid
- Trigonometry-Sine Ratio
- Trigonometry-Cosine Ratio
- Trigonometry-Tangent Ratio
- Using Similar Triangles in Indirect Measurement
- Using Trigonometry in Indirect Measure
- Quiz 3: Triangles and Trigonometry
- Test
- Alternate Test
- Glossary and Credits

##### UNIT 6 – SEMESTER REVIEW AND EXAM

- Review
- Exam
- Alternate Exam—Form A
- Alternate Exam—Form B