Geometry A Course Syllabus

Course Description
Geometry A, the first course of a two-semester series, teaches students the logic and information they will need to solve proof problems and to prove mathematical theorems. Emphasis in this course is on the logic of geometry, angles and lines, triangles and congruency, quadrilaterals, similarity, and right triangles. Students enrolling in this course should have successfully completed one year of Algebra.

Course Objectives
Upon completion of this course, you will be able to:

·  use conditional statements, inductive and deductive reasoning, and algebraic properties to solve geometric proofs

·  identify the angles formed by parallel lines and transversals

·  classify triangles by side length and angle measure

·  prove triangles are congruent by SSS, SAS, AAS, and ASA

·  identify special quadrilaterals and use their properties to find missing measures

·  use proportions to determine similarity and find missing measures of similar figures

·  use Pythagorean Theorem, properties of special right triangles and ratios from trigonometry to find missing measures of right triangles

*NOTE: The suggested time frame for the completion of each unit is just an estimate. This syllabus is based on an 18-week semester. You may work on each unit at your own pace, but keep in mind that you must finish the entire course within the time specified by your school district.

Unit 1: Logic of Geometry (Weeks 1 through 2)
Objectives:
Upon completion of this unit, you will be able to:

·  describe the undefined terms of Geometry

·  use the undefined terms to define other vocabulary terms

·  write conditional (if-then) statements

·  write the converse of conditional statements

·  write the inverse of conditional statements

·  write the contrapositive of conditional statements

·  apply the properties of Algebra in geometry

·  write simple geometric proofs

Modules:

  1. Geometry Basics - Vocabulary
  2. Points, Lines, Planes, and Space Video
  3. Vocabulary – Angles
  4. Vocabulary – Figures and Reasoning
  5. Thinking About Geometry Video
  6. Postulates and Theorems Video
  7. Logic of Geometry
  8. Conjectures and Inductive Reasoning
  9. Counterexample
  10. Conditional (If-Then) Statements
  11. eview Exercises
  12. Related Conditionals
  13. Conditional Statements Gizmo
  14. Inverse
  15. Contrapositive
  16. Review Exercises
  17. Deductive Reasoning
  18. Laws of Deductive Reasoning
  19. Review Exercises
  20. Algebraic Properties – Addition and Subtractions
  21. Algebraic Properties – Multiplication and Division
  22. Properties of Equality and Congruence – Reflexive and Symmetric
  23. Properties of Equality and Congruence – Transitive and Substitution
  24. Review Exercises

Assignments:

Lesson 1 Homework - Conjectures and Inductive Reasoning / Homework / 5 points
Lesson 2 Homework - Related Conditionals / Homework / 5 points
Lesson 3 Homework - Deductive Reasoning / Homework / 5 points
Lesson 4 Homework - Algebraic Properties Used in Geometry / Homework / 5 points
Unit 1 Test – Logic of Geometry / Exam / 10 points


Unit 2: Angles and Lines (Weeks 3 through 5)
Objectives:
Upon completion of this unit, you will be able to:

·  identify and name pairs of angles

·  identify angles formed by transversals

·  apply properties of parallel lines

·  use proofs to prove lines are parallel

·  apply properties of parallel lines to prove special triangle relationships

·  apply properties of perpendicular lines

·  identify, name and find the sum of the angles of polygons

Modules:

  1. Angles and Lines
  2. Angle Pairs – Adjacent Angles
  3. Angle Pairs –Complementary Angles
  4. Angle Pairs – Supplementary Angles
  5. Angle Pairs – Vertical Angles
  6. Investigating Angle Theorems Gizmos
  7. Proof Exercises
  8. Angles Defined Video
  9. Review Exercises
  10. Transversal
  11. Review Exercises
  12. Parallel Lines and Transversals – Corresponding Angles
  13. Alternate Interior Angles
  14. Proof Exercise – Alternate Interior Angle Theorem
  15. Alternate Exterior Angles
  16. Proof Exercise – Alternate Exterior Angle Theorem
  17. Same-Side Interior Angles
  18. Proof Exercise – Same-Side Interior Angle Theorem
  19. Perpendicular Transversal
  20. Review Exercises
  21. Proving Parallel Lines – Corresponding Angles
  22. Proving Parallel Lines – Alternate Interior Angles
  23. Proof Exercise – Converse of the Alternate Interior Angles Theorem
  24. Proving Parallel Lines – Alternate Exterior Angles
  25. Proof Exercise – Converse of Alternate Exterior Angle Theorem
  26. Proving Parallel Lines – Same-Side Interior Angles
  27. Proving Parallel Lines – Other Methods
  28. Proving Parallel Lines – Review
  29. Parallel Lines and Angles Video
  30. Review Exercises
  31. Perpendicular Lines
  32. Construction – Perpendicular Lines through a Point on a Given Line
  33. Perpendicular Lines and Linear Pairs and Perpendicular Postulate
  34. Construction - Perpendicular Lines through a Point Not on a Given Line
  35. Proof Exercise – Perpendicular Lines and Complementary Angles
  36. Review Exercises

Assignments:

Lesson 1 Homework - Angle Pairs / Homework / 5 points
Lesson 2 Homework – Transversals / Homework / 5 points
Lesson 3 Homework – Parallel Lines and Transversals / Homework / 5 points
Lesson 4 Homework – Proving Parallel Lines / Homework / 5 points
Lesson 5 Homework – Perpendicular Lines / Homework / 5 points
Unit 2 Test – Angles and Lines / Exam / 10 points


Unit 3: Triangles and Congruency (Weeks 6 through 8)
Objectives:
Upon completion of this unit, you will be able to:

·  Classify triangles by the length of their sides

·  Classify triangles by the measure of their angles

·  Find the corresponding parts of congruent triangles

·  Apply postulates and theorems to prove triangle congruency

·  Use medians, altitudes and bisectors to explore special relationship in triangles

Modules:

  1. Construction Tools
  2. Triangles and Congruency
  3. Classifying Triangles by Sides and Angles – Classifying Triangles Gizmo
  4. Classifying by Sides
  5. Isosceles and Equilateral Triangles Gizmo
  6. Proof Exercise – Isosceles Triangle Theorem
  7. Classifying by Angles
  8. Review Exercises
  9. Special Triangle Relationship using Parallel Lines
  10. Triangle Sum Theorem
  11. Proof Exercise – Triangle Sum Theorem
  12. Triangle Angle Sum Activity A & B Gizmo
  13. Third Angle Theorem
  14. Exterior Angle Theorem
  15. Triangles – Definitions and Basic Facts Video
  16. Review Exercises
  17. Congruent Triangles and their Corresponding Parts
  18. Corresponding Parts of Congruent Triangles
  19. Construction – Congruent Segments
  20. Construction – Congruent Angle
  21. Properties of Triangle Congruence
  22. Definition of Congruent Triangles (CPCTC)
  23. Review Exercises
  24. Theorems and Postulates for Triangle Congruency
  25. Side-Side-Side Postulate (SSS)
  26. Side-Angle-Side Postulate (SAS)
  27. Angle-Side-Angle Postulate (ASA)
  28. Angle-Angle-Side Theorem (AAS)
  29. Proof Exercise – Angle-Angle-Side Theorem
  30. Review of Triangle Congruency
  31. Proving Triangles Congruent Video
  32. Proving Triangles Congruent Gizmo
  33. Review Exercises
  34. Special Relationships in Triangles
  35. Bisectors, Medians and Altitudes
  36. Bisector Discussion (Part 1) – Bisectors in Triangles Gizmo
  37. Bisector Discussion (Part 2) – Perpendicular Bisector and Paper Construction
  38. Bisector Discussion (Part 3) – Circumcenter Theorem and Paper Construction
  39. Bisector Discussion (Part 4) – Angle Bisector Theorem and Incenter Theorem
  40. Median Discussion
  41. Altitude Discussion
  42. Review of Special Relationships in Triangles
  43. Concurrent Lines, Medians, and Altitudes Gizmo
  44. Review Exercises

Assignments:

Lesson 1 Homework - Classifying Triangles by Sides and Angles / Homework / 5 points
Lesson 2 Homework – Special Triangles and Their Corresponding Parts / Homework / 5 points
Lesson 3 Homework – Congruent Triangles and Their Corresponding Parts / Homework / 5 points
Lesson 4 Homework – Theorems and Postulates for Triangle Congruency / Homework / 5 points
Lesson 5 Homework – Special Relationships in Triangles / Homework / 5 points
Unit 3 Test – Triangles and Congruency / Exam / 10 points


Geometry A Midterm Exam (Week 9)
Objectives:
Upon completion of this unit, you will be able to:

·  review information acquired and mastered from this course up to this point

·  take a course exam based on material from the first three units in this course (Note: You will be able to open this exam only one time.)

Assignment:

Geometry A Midterm Exam / Exam / 18 points


Unit 4: Quadrilaterals (Weeks 10 through 12)
Objectives:
Upon completion of this unit, you will be able to:

·  classify polygons by number of sides

·  calculate the sum of the interior angles of a polygon

·  identify parts of quadrilaterals and find the sum of their interior angles

·  show, identify and apply the properties of parallelograms

·  determine if a quadrilateral is a parallelogram

·  identify and apply properties of special parallelograms

·  identify and apply properties of trapezoids

·  prove congruent quadrilaterals

Modules:

  1. Polygons
  2. Convex Polygon and Concave Polygon
  3. Polygon Angle Sum Activity A & B Gizmos
  4. Interior and Exterior Angle Theorem
  5. General Definitions of Polygons Video
  6. Review Exercises
  7. Identifying Parts of and Types of Quadrilaterals
  8. Part of a Quadrilateral
  9. Quadrilateral Chart
  10. Review Exercises
  11. Parallelograms
  12. Properties of Parallelograms (Theorems) Part 1
  13. Proof Exercise – Opposite Angles of a Parallelogram are Congruent
  14. Properties of Parallelograms (Theorems) Part 2
  15. Proof Exercise – Consecutive Angles in a Parallelogram are Supplementary
  16. Properties of Parallelograms (Theorems) Part 3
  17. Proof Exercise – Diagonals of a Parallelogram and Congruent Triangles
  18. Test for Parallelograms
  19. Parallelogram Conditions Gizmo
  20. Ways to Prove a Quadrilateral is a Parallelogram
  21. Review Exercises
  22. Classifying Quadrilaterals – Activity A Gizmo
  23. Special Parallelograms
  24. Rectangle and its Diagonals
  25. Proof Exercise – Diagonals of a Rectangle
  26. Rhombus and its Diagonals
  27. Special Quadrilaterals Gizmo
  28. Squares
  29. Review Exercises
  30. Trapezoids and Kites
  31. Trapezoids
  32. Isosceles Trapezoid
  33. Median (AKA Midsegment) of a Trapezoid
  34. Kites
  35. Classifying Quadrilaterals – Activity B Gizmo
  36. Review Exercises

Assignments:

Lesson 1 Homework – Polygons / Homework / 5 points
Lesson 2 Homework – Identifying Parts of and Types of Quadrilaterals / Homework / 5 points
Lesson 3 Homework – Parallelograms / Homework / 5 points
Lesson 4 Homework – Special Parallelograms / Homework / 5 points
Lesson 5 Homework – Trapezoids and Kites / Homework / 5 points
Unit 4 Test – Quadrilaterals / Exam / 10 points


Unit 5: Similarity (Weeks 13 through 14)
Objectives:
Upon completion of this unit, you will be able to:

·  use ratios and proportions to solve geometric problems

·  apply properties of proportions

·  identify and apply theorems about similar polygons including triangles

·  identify and use the relationship between proportional parts of triangles which includes the Triangle Proportionality Theorem

Modules:

  1. Ratios and Proportions
  2. Definition of Ratio
  3. Ratios Video
  4. Simplifying Ratios and Using Ratios
  5. Extended Ratios
  6. Proportion
  7. Cross Product Property
  8. Proportions and Common Multipliers Gizmo
  9. Reciprocal Property and Solving Proportions
  10. Beam to Moon (Ratios and Proportion) Gizmo
  11. Review Exercises
  12. Similar Polygons
  13. Similar Pentagons Example
  14. Scale Factor
  15. Similar Figures – Activity A Gizmo
  16. Similar Polygons Gizmo
  17. Perimeters of Similar Polygons Theorem
  18. Using Proportions with Similar Polygons
  19. Review Exercises
  20. Similar Triangles
  21. Angle-Angle Similarity Postulate
  22. Side-Side-Side Similarity Postulate
  23. Side-Angle-Side Similarity Postulate
  24. Part 2 – Special Triangles Video
  25. Section A – Proving the Similarity of Triangles Video
  26. Review Exercises
  27. Proportionality Theorems
  28. Triangle Proportionality Theorem
  29. Converse to the Triangle Proportionality Theorem
  30. Midsegment Theorem
  31. Parallel Proportionality Theorem
  32. Review Exercises

Assignments:

Lesson 1 Homework – Ratios and Proportions / Homework / 5 points
Lesson 2 Homework – Similar Polygons / Homework / 5 points
Lesson 3 Homework – Similar Triangles / Homework / 5 points
Lesson 4 Homework –Proportionality Theorems / Homework / 5 points
Unit 5 Test – Similarity / Exam / 10 points


Unit 6: Right Triangles (Weeks 15 through 17)
Objectives:
Upon completion of this unit, you will be able to:

·  determine similarity of right triangles

·  simplify square roots

·  apply the concept of geometric mean and use the ratios formed by the geometric mean theorems

·  apply the Pythagorean Theorem and its converse to right triangles

·  apply the properties of special right triangles to find the lengths of the sides

·  apply trigonometric ratios and their inverses to solve problems

Modules:

  1. Congruency of Right Triangles
  2. Congruence Theorems for Right Triangles – Part 1
  3. Congruence Theorems for Right Triangles – Part 2
  4. Review Exercises
  5. Similar Right Triangles
  6. Altitude of a Right Triangle
  7. Geometric Mean
  8. Geometric Mean Theorems
  9. Similarity in Right Triangles Gizmo
  10. Review Exercises
  11. Square Roots
  12. Square Roots Gizmo
  13. Multiplying and Dividing Square Roots
  14. Simplifying Radicals – Activity A Gizmo
  15. Review Exercises
  16. The Pythagorean Theorem and its Converse
  17. The Converse of the Pythagorean Theorem
  18. Pythagorean Theorem – Activity A Gizmo
  19. Right Triangles, Altitudes, the Pythagorean Theorem, and You Video
  20. Pythagorean Theorem – Activity B Gizmo
  21. Review Exercises
  22. Special Right Triangles
  23. 45°-45°-90° Right Triangle Theorem
  24. 30°-60°-90° Right Triangle Theorem
  25. Special Right Triangles Video
  26. Review Exercises
  27. Right Triangles and Trigonometric Ratios
  28. Sine, Cosine, and Tangent (Basic Trig Ratios)
  29. Sine, Cosine, and Tangent Gizmo
  30. Sine and Cosine Ratios – Activity A Gizmo
  31. Sine and Cosine Ratios – Activity B Gizmo
  32. Tangent Ratio Gizmo
  33. Cosecant, Secant, and Cotangent (Inverses of Basic Trig Ratios)
  34. Six Trig Functions Video
  35. Trigonometric Values of Special Angles
  36. Trigonometric Values Video
  37. Review Exercises

Assignments:

Lesson 1 Homework – Congruency of Right Triangles / Homework / 5 points
Lesson 2 Homework – Similar Right Triangles / Homework / 5 points
Lesson 3 Homework – Square Roots / Homework / 5 points
Lesson 4 Homework – The Pythagorean Theorem and its Converse / Homework / 5 points
Lesson 5 Homework – Special Right Triangles / Homework / 5 points
Lesson 6 Homework – Right Triangles and Trigonometric Ratios / Homework / 5 points
Unit 6 Test – Right Triangles / Exam / 10 points


Geometry A Final Exam (Week 18)Objectives:
Upon completion of this unit, you will be able to:

·  review information acquired and mastered from this course

·  take a course exam based on material from all units in this course (Note: You will be able to open this exam only one time.)

Assignment:

Geometry A Final Exam / Exam / 25 points

Disability Statement
If you have a disability or condition that may affect your ability to succeed in this course, please contact your teacher. It’s important that you discuss the problem with him or her so accommodations may be made to give you every opportunity to perform well. Your teacher and virtual school program coordinators are committed to helping students with disabilities succeed, and every request will be treated with respect and confidentiality.

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