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GEOMETRY ACADEMIC LIBRARY 

First Semester

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Geometry Online

​Geometry is a full year, high school math course for the student who has successfully completed the prerequisite course, Algebra I. The course focuses on the skills and methods of linear, coordinate, and plane geometry.

These supplementary videos are in addition to the video instruction of your online lessons and work with the Academy teachers. They are not the curriculum but are aligned to the daily lesson material. Students should work in their online curriculum, with their NFC Academy teacher and use these videos in their learning process as needed.

2nd Semester Geometry
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Geometry Online First Semester

UNIT 1 – INTRODUCTION
  1. ​​​Course Overview
  2. ​Mathematics System: Set Theory Review  
    1. Introduction to Set Theory
    2. Introduction to Subsets
    3. Intersection and Union of Sets 
    4. Relative Complement of Difference Between Sets  
    5. Universal Set and Absolute Complement 
    6. Subset, Strict Subset, and Super Set 
    7. Bringing the Set Operations Together 
  3. ​Mathematics System: Operations with Sets
    1. Set Operations and Venn Diagrams – Part 1 of 2
    2. Set Operations and Venn Diagrams – Part 2 of 2
  4. Quiz 1: Set Theory
  5. Geometry Undefined Terms: Point
    1. Point, Line, Plane 
    2. Lesson 1-1: Point, Line, Plane
    3. Geometry Lesson 1 – Building Blocks of Geometry
    4. Language and Notation of Basic Geometry 
    5. Lines, Line Segments, and Rays 
    6. Drawing Lines Exercise Examples  
    7. Drawing Lines 
  6. ​Geometry Undefined Terms: Line
    1. Point, Line, Plane
    2. Lesson 1-1: Point, Line, Plane
    3. Geometry Lesson 1 – Building Blocks of Geometry​
  7. Geometry Undefined Terms: Plane
    1. Point, Line, Plane
    2. Lesson 1-1: Point, Line, Plane
    3. Geometry Lesson 1 – Building Blocks of Geometry
  8. Quiz 2: Undefined Terms
  9. Defined Terms: Definitions
    1. Specifying Planes in Three Dimensions 
  10. Quiz 3: Defined Terms
  11. Geometric Postulates
    1. Language and Notation of Basic Geometry  (The student will use concepts covered in this basic review of geometric terms throughout the course) 
    2. Definitions, Postulates and Theorems
  12. Review of Algebraic Postulates
  13. Geometric Theorems
    1. ​Geometry Lesson: Postulates, Theorems and Proofs
  14. ​Review of Properties of Algebra
    1. Commutative Law of Addition 
    2. Associative Law of Addition 
    3. Inverse Property of Addition 
    4. Commutative Law of Multiplication 
    5. Associative Law of Multiplication 
    6. Inverse Property of Multiplication
  15. Quiz 4: Postulates and Theorems
  16. Test
  17. Alternate Test
  18. Glossary and Credits
UNIT 2 – LOGIC
  1. ​Logic
    1. Conditional Statements and Deductive Reasoning 
    2. Logical Argument and Deductive Reasoning Exercise 
  2. Conjunctions
    1. Conjunctions, Disjunctions, and Negations
    2. Geometry – Conjunctions and Disjunctions
    3. 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.)
    4. Introduction to Logic
    5. Mathematical Statements and Truth Value
  3. Disjunctions
    1. Conjunctions, Disjunctions, and Negations (Repeat)
    2. Geometry – Conjunctions and Disjunctions
  4. Negation
    1. Conjunctions, Disjunctions, and Negations
    2. Geometry – Conjunctions and Disjunctions
  5. Conditional or Implication Statements
    1. Geometry Conditional Statement
    2. Logic -Conditional Statements
    3. Truth Tables for Conditional Statements and Biconditional Statements
    4. Conditional Statements
  6. Converse, Inverse, Contrapositive
    1. Converse, Inverse, Contrapositive 
  7. Quiz 1: Principles of Logic
  8. ​Counterexamples
    1. Counterexamples
  9. Inductive Reasoning
    1. Difference Between Inductive Reasoning and Deductive Reasoning 
    2. Inductive Reasoning
  10. Deductive Reasoning
    1. Geometry Deductive Reasoning 
    2. Deductive Reasoning
  11. Using Deductive Reasoning
    1. Geometry Deductive Reasoning 
  12. Quiz 2: Inductive and Deductive Reasoning
  13. 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)
    1. Two Column Proof Showing Segments are Perpendicular
    2. Two Column Proof 
    3. Using If – Then Logic
  14. ​Proof Formats: The Figure
    1. Two Column Proof Showing Segments are Perpendicular 
    2. ​Two Column Proof  ​
  15. Proof Formats: The Given Statement
  16. Proof Formats: To Prove Statement
  17. Proof Formats: The Plan of the Proof
  18. ​Indirect Proof Format: The Paragraph Proof
    1. Indirect Proof 
  19. Quiz 3: Proof Formats​​
  20. Test
  21. Alternate Test
  22. Glossary and Credits
UNIT 3 – ANGLES AND PARALLELS
  1. Angle Definitions
    1. Angle Basics 
  2. Angle Measurement
    1. Measuring Angles in Degrees 
    2. Using a Protractor 
  3. Quiz 1: Angles
  4. Geometric Proof
    1. Geometry Proofs: Two Column Proofs
    2. Two Column Proofs: Lesson (Geometry Concepts)
  5. Angle Relationship Definitions
    1. Complementary and Supplementary Angles 
    2. Complementary and Supplementary Angles 
    3. Vertical, Adjacent, and Linearly Paired Angles 
    4. Complimentary, Supplementary and Vertical Angles
    5. Identify Adjacent Angles
  6. Angle Relationship Theorems (1)
    1. Complementary and Supplementary Angles
    2. Vertical Angles
  7. Angle Relationship Theorems (2)
    1. Congruent Complements 
    2. Congruent Supplements
    3. Properties of Perpendicular Lines
  8. Quiz 2: Angle Theorems
  9. Construction: Copying Figures
  10. Construction: Bisecting Figures 
  11. Basic Properties of Parallels
    1. Angles Formed by Parallel Lines and Transversals 
    2. Identifying Parallel and Perpendicular Lines  
  12. ​Transversals and Special Angles
    1. Finding Out Angeles Between Transversals and Parallel Lines
    2. Parallel Lines and Transversals  
    3. Parallel Lines and Transversals
  13. More Proofs: Transversals and Special Angles (Students should use the previous instructional presentations for their work in this lesson)
  14. Continued Proofs: Transversals and Special Angles (Students should use the previous instructional presentations for their work in this lesson)
  15. More Proofs for Postulates 9 and 10– (Students should use the previous instructional presentations for their work in this lesson)
  16. Quiz 3: Parallels and Transversals
  17. Construction: Perpendiculars
  18. Construction: Tangents to Circles
  19. Construction: Parallels
  20. Classifying Triangles by Sides and Angles
    1. Classifying Shapes Scalene, Isosceles, Equilateral, Acute, Right, Obtuse Triangles 
    2. Congruent Legs and Base Angles of Isosceles Triangle 
    3. Equilateral Triangle Sides and Angles Congruent 
  21. Exterior and Remote Interior Angles of a Triangle
    1. Exterior and Remote Angles of a Triangle
    2. The Remote Exterior Angle Theorem
  22. Proofs Involving Triangles
    1. Introduction to Interior and Exterior Angles of a Triangle
    2. Proof: The Exterior Angle Theorem  ​
  23. Other Polygons
    1. ​Sum of Interior Angles of a Polygon 
  24. Quiz 4: Triangles, Polygons, and Angle Properties
  25. ​​Test
  26. Alternate Test
  27. Glossary and Credits
UNIT 4 – CONGRUENT TRIANGLES AND QUADRILATERALS
  1. ​​Defining Congruent Triangles
    1. Congruent Triangles and SSS 
    2. Finding Congruent Triangles 
    3. Other Triangle Congruence Postulates 
  2. Proving Triangles Congruent (1)
    1. Congruent Triangle Proof Example 
    2. Congruent Triangle Proof Example 2 
  3. ​Proving Triangles Congruent (2)
  4. Proving Triangles Congruent (3)
  5. Proving Right Triangles Congruent
    1. Right Triangle Congruence Theorems
    2. Congruence in Right Triangles
    3. Right Triangle Congruence 
  6. Quiz 1: Congruent Triangles
  7. Independent Triangles (1)
    1. Other Triangle Congruence Postulates – Review 
    2. Finding Congruent Triangles – Review 
    3. Congruent Triangle and Reflexive Property
  8. Independent Triangles (2)
  9. Overlapping Triangles (1)
    1. Congruent Overlapping Triangles
    2. Proofs Overlapping Triangles
    3. Congruence in Overlapping Triangles 
  10. Overlapping Triangles (2)
  11. Isosceles Triangles (1)
    1. Congruent Legs and Base Angles of Isosceles Triangles 
    2. The Isosceles Triangle Theorem
  12. Isosceles Triangles (2)
  13. 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)
  14. Construction of Triangles 45-45-90
  15. Constructing Inscribed Shapes
    1. ​​​​Constructions: circle inscribed square
    2. ​Constructions: circle inscribed equilateral triangle
    3. Constructions: circle inscribed regular hexagon 
  16. Quiz 2: Types of Triangles
  17. Inequality Theorem in One Triangle Part 1
    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) 
    2. Triangle Inequality Theorem
    3. Triangle Inequality Theorem
  18. Inequality Theorem in One Triangle Part 2 (Use the instructional presentations from the previous assignment as needed for this current lesson)
  19. Inequality Theorem in Two Triangles
    1. Inequalities of Two Triangles and Indirect Proof
  20. Quadrilateral Parallelograms Theorems Part 1
    1. Quadrilateral Overview 
    2. Opposite Sides of a Parallelogram Congruent 
    3. Proof Diagonals of Parallelogram Bisect Each Other 
    4. Proof Opposite Angles of Parallelogram Congruent 
    5. Area of Parallelogram 
    6. I am a Parallelogram (Have some fun with this one) 
  21. Quadrilateral Parallelograms Theorems Part 2  (Use the instructional presentations from the previous assignment as needed for this current lesson)
  22. Quiz 3: Inequalities; Quadrilaterals
  23. Triangles that Use Parallelograms in Proofs  (Review any of the instructional presentations in the previous section as needed for this lesson)
  24. Parallelograms: Rectangles
    1. Properties of Special Parallelograms – Rhombus, Rectangles, and Square
    2. Rhombus, Square, Parallelogram and Rectangle 
  25. Parallelograms: Rhombus
    1. Proof – Rhombus Diagonals  Are Perpendicular Bisectors 
  26. Trapezoids-Definitions and Proofs
    1. Properties and Parts of Trapezoids
    2. Median of Trapezoid
    3. Quadrilateral Overview – Back to this presentation which will cover a Trapezoid 
    4. What Is an Isosceles Trapezoid? 
  27. Quiz 4: Parallelograms; Trapezoids
  28. ​​Test
  29. Alternate Test
  30. Glossary and Credits
UNIT 5 – SIMILAR POLYGONS
  1. ​Algebra and Ratios
    1. Introduction to Ratios – Review 
    2. Ratios as Fractions In Simplest Form – Review 
    3. Simplifying Rates and Ratios – Review 
  2. Algebra Properties and Proportions
    1. Ratios and Proportions
    2. Ratios and Proportions Movie (Short)
  3. Properties of Proportions
    1. The Golden Ratio 
    2. The Golden Ratio ​
  4. Quiz 1: Ratios, Properties, and Proportions
  5. Meaning of Similarity
    1. Similarity Postulates 
    2. Intro to triangle similarity    
  6. Meaning of Similarity-Theorems
    1. Similar Triangle Example Problems 
    2. Similarity Example Problems 
    3. Similarity Where Same Sides Play Different Roles 
  7. Meaning of Similarity-Proofs
    1. Similar Triangle Example Problems
    2. Similarity Example Problems 
    3. Similarity Where Same Sides Play Different Roles  
  8. Theorems-Similar Polygons
    1. Similar Figures and Proportions
    2. Similar Polygons
    3. Similar Polygons
    4. Similar Polygons
  9. Theorems-Special Segments in Triangles
    1. Proportions in Triangles
    2. Geometry Proportions in Triangles
    3. Side Splitter Theorem Proportions in Triangles 
  10. Similar Right Triangles
    1. Right Triangle Similarity and Geometric Mean
    2. Similar Right Triangles
  11. The Pythagorean Theorem
    1. The Pythagorean Theorem 
    2. The Pythagorean Theorem Intro 
  12. Theorem about 30-60-90 Right Triangles
    1. 30-60-90 Triangle Sides Ratio Proof
  13. Theorem about 45-45-90 Right Triangles
    1. 45-45-90 Triangle Side Ratios 
  14. Quiz 2: Similarity; Triangle Theorems
  15. Using Triangles: Rectangular Solids
    1. Shapes, Faces, Edges, and Vertices
    2. What is the Face of a Prism?
  16. Using Triangles: Regular Square Pyramid
    1. Surface Area of Square Based Pyramids
  17. Trigonometry-Sine Ratio
    1. Proof Law of Sines 
    2. Trigonometry Ratios Sine
  18. Trigonometry-Cosine Ratio
    1. Law of Cosines Example
    2. Proof of the Law of Cosines 
  19. Trigonometry-Tangent Ratio
    1. Intro to Trigonometry Ratios  ​
  20. Using Similar Triangles in Indirect Measurement
    1. Indirect Measurement Using Similar Triangles
    2. Why Similar Triangles Can Be Used For Indirect Measurement
  21. Using Trigonometry in Indirect Measure
    1. Using Trig Ratios to Solve Problems
    2. Determine the Height of an Object Using A Trigonometry Equation (Tangent equation)
    3. Finding the Height of an Object Using Trigonometry (Tangent)
  22. Quiz 3: Triangles and Trigonometry
  23. Test
  24. Alternate Test
  25. Glossary and Credits
UNIT 6 – SEMESTER REVIEW AND EXAM
  1. Review
  2. Exam
  3. Alternate Exam—Form A
  4. Alternate Exam—Form B