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1 This image cannot currently be displayed. Course Catalog Geometry 2016 Glynlyon, Inc.

2 Table of Contents COURSE OVERVIEW... 1 UNIT 1: INTRODUCTION... 1 UNIT 2: LOGIC... 1 UNIT 3: ANGLES AND PARALLELS... 2 UNIT 4: CONGRUENT TRIANGLES AND QUADRILATERALS... 2 UNIT 5: SIMILAR POLYGONS... 2 UNIT 6: SEMESTER REVIEW AND EXAM... 2 UNIT 7: CIRCLES... 3 UNIT 8: AREA AND VOLUME... 3 UNIT 9: COORDINATE... 3 UNIT 10: TRANSFORMATIONS... 3 UNIT 11: REVIEW... 4 UNIT 12: SEMESTER REVIEW AND EXAM... 4 UNIT 13: FINAL EXAM... 4 i 2016 Glynlyon, Inc.

3 COURSE OVERVIEW 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. In it, students will gain solid experience with geometric calculations and coordinate plane graphing, methods of formal proof, and techniques of construction. By the end of the course, students will be expected to do the following: Understand defined terms, axioms, postulates, and theories. Apply rules of formal logic and construct proofs in two-column format. Know how to solve for angles given parallels, perpendiculars, and transversals. Demonstrate how to solve for sides and angles of triangles, quadrilaterals, and polygons. Understand trigonometric ratios and know how to use them to solve for unknown sides and angles in given triangles as well as application word problems. Be able to determine arcs, chords, and sectors of circles. Calculate perimeter, area, and volume of figures and solids. Graph lines and determine slopes, midpoints, and distances. Make geometric constructions on paper. Represent results of motion geometry (translation, rotation, reflection, dilation). UNIT 1: INTRODUCTION 1. Course Overview 11. Geometric Postulates 2. Mathematic System: Set Theory Review 12. Review of Algebraic Postulates 3. Mathematic System: Operations with Sets 13. Geometric Theorems 4. Quiz 1: Set Theory 14. Review of Properties of Algebra 5. Geometry Undefined Terms: Point 15 Quiz 4: Postulates and Theorems 6. Geometry Undefined Terms: Line 16. Special Project* 7 Geometry Undefined Terms: Plane 17. Test 8. Quiz 2: Undefined Terms 18. Alternate Test* 9. Defined Terms: Definitions 19. Glossary and Credits 10. Quiz 3: Defined Terms UNIT 2: LOGIC 1. Logic 12. Proof Formats: Statement of the Theorem 2. Conjunctions 13. Proof Formats: The Figure 3. Disjunctions 14. Proof Formats: The Given Statement 4. Negation 15. Proof Formats: To Prove Statement 5. Conditional or Implication Statements 16. Proof Formats: The Plan of the Proof 6. Converse, Inverse, Contrapositive 17. Indirect Proof Format: The Paragraph Proof 7. Quiz 1: Principles of Logic 18. Quiz 3: Proof Formats 8. Inductive Reasoning 19. Special Project* 9. Deductive Reasoning 20. Test 10. Using Deductive Reasoning 21. Alternate Test* 11. Quiz 2: Inductive and Deductive Reasoning 22. Glossary and Credits Glynlyon, Inc.

4 UNIT 3: ANGLES AND PARALLELS 1. Angle Definitions 15. Quiz 3: Parallels and Transversals 2. Angle Measurement 16. Construction: Perpendiculars 3. Quiz 1: Angles 17 Construction: Tangents to Circles 4. Angle Relationship Definitions 18. Construction: Parallels 5. Angle Relationship Theorems (1) 19. Classifying Triangles by Sides and Angles 6. Angle Relationship Theorems (2) 20. Exterior and Remote Interior Angles of a 7. Quiz 2: Angle Theorems Triangle 8. Construction: Copying Figures 21. Proofs Involving Triangles 9. Construction: Bisecting Figures 22. Other Polygons 10. Basic Properties of Parallels 23. Quiz 4: Triangles, Polygons, and Angle 11. Transversals and Special Angles Properties 12. More Proofs: Transversals and Special Angles 24. Special Project* 13. Continued Proofs: Transversals and Special 25. Test Angles 26. Alternate Test* 14. More Proofs for Postulates 9 and Glossary and Credits UNIT 4: CONGRUENT TRIANGLES AND QUADRILATERALS 1. Defining Congruent Triangles 16. Inequality Theorem in One Triangle Part 2 2. Proving Triangles Congruent (1) 17. Inequality Theorem in Two Triangles 3. Proving Triangles Congruent (2) 18. Quadrilateral Parallelograms Theorems Part 1 4. Proving Right Triangles Congruent 19. Quadrilateral Parallelograms Theorems Part 2 5. Quiz 1: Congruent Triangles 20. Quiz 3: Inequalities; Quadrilaterals 6. Independent Triangles (1) 21. Triangles that Use Parallelograms in Proofs 7. Independent Triangles (2) 22. Parallelograms: Rectangles 8. Overlapping Triangles (1) 23. Parallelograms: Rhombus 9. Overlapping Triangles (2) 24. Trapezoids-Definitions and Proofs 10. Isosceles Triangles (1) 25. Quiz 4: Parallelograms; Trapezoids 11. Isosceles Triangles (2) 26. Special Project* 12. Construction of Triangles Test 13. Construction of Triangles Alternate Test* 14. Quiz 2: Types of Triangles 29. Glossary and Credits 15. Inequality Theorem in One Triangle Part 1 UNIT 5: SIMILAR POLYGONS 1. Algebra and Ratios 15. Using Triangles: Rectangular Solids 2. Algebra Properties and Proportions 16. Using Triangles: Regular Square Pyramid 3. Properties of Proportions 17. Trigonometry-Sine Ratio 4. Quiz 1: Ratios, Properties, and Proportions 18. Trigonometry-Cosine Ratio 5. Meaning of Similarity 19. Trigonometry-Tangent Ratio 6. Meaning of Similarity-Theorems 20. Using Similar Triangles in Indirect Measurement 7. Meaning of Similarity-Proofs 21. Using Trigonometry in Indirect Measure 8. Theorems-Similar Polygons 22. Quiz 3: Triangles and Trigonometry 9. Theorems-Special Segments in Triangles 23. Project: Model and Scale Drawing 10. Similar Right Triangles 24. Special Project* 11. The Pythagorean Theorem 25. Test 12. Theorem about Right Triangles 26. Alternate Test* 13. Theorem about Right Triangles 27. Glossary and Credits 14. Quiz 2: Similarity; Triangle Theorems UNIT 6: SEMESTER REVIEW AND EXAM 1. Review 3. Alternate Exam - Form A* 2. Exam 4. Alternate Exam - Form B* Glynlyon, Inc.

5 UNIT 7: CIRCLES 1. Characteristics of Circles 11. Special Angles Type 2 2. Characteristics of Spheres 12. Special Angles Type 3 3. Quiz 1: Circles and Spheres 13. Special Segments 4. Tangents 14. Quiz 3: Special Angles and Segments 5. Arcs 15. Construction: Circles 6. Chords 16. Special Project* 7. Theorems (1) 17. Test 8. Theorems (2) 18. Alternate Test* 9. Quiz 2: Tangents, Arcs, and Chords 19. Glossary and Credits 10. Special Angles Type 1 UNIT 8: AREA AND VOLUME 1. Area Concepts of Polygons 15. Solids: Prisms 2. Area of Rectangles 16. Solids: Pyramids 3. Area of Parallelograms 17. Solids: Cylinders 4. Area of Triangles and Rhombuses 18. Solids: Cones 5. Area of Trapezoids 19. Solids: Spheres 6. Area of Regular Polygons 20. Quiz 3: Volume of Solids 7. Area Comparisons of Polygons 21. Construction: Dividing a Segment 8. Quiz 1: Area of Polygons 22. Construction: 4th Proportion 9. Construction: Polygons 23. Construction: The Geometric Mean 10. Circles: Circumference and PI 24. Special Project* 11. Circles: Area of Circles 25. Test 12. Circles: Area of Sectors 26. Alternate Test* 13. Circles: Area of Segments 27. Glossary and Credits 14. Quiz 2: Area of Circles UNIT 9: COORDINATE 1. Symmetry 11. Equations of Lines 2. Ordered Pairs: Points in a Plane 12. Quiz 3: Slope and Lines 3. Graphs of Algebraic Sentences 13. Figures in the Coordinate Plane 4. Quiz 1: Symmetry, Ordered Pairs, and Graphs 14. Proofs with Coordinate Geometry (1) 5. Distance Formula 15. Proofs with Coordinate Geometry (2) 6. Equation of a Circle 16. Quiz 4: Figures and Proofs 7. Midpoint Formula 17. Special Project* 8. Quiz 2: Distance Formula and Applications 18. Test 9. Slope 19. Alternate Test* 10. Parallel and Perpendicular Lines 20. Glossary and Credits UNIT 10: TRANSFORMATIONS 1. Introduction: Rigid Motion, or Isometry 8. Inverse and Identity Transformation 2. Isometry: Reflection 9. Quiz 2: Transformations 3. Isometry: Translation 10. Special Project* 4. Isometry: Rotation 11. Test 5. Quiz 1: Isometry 12. Alternate Test* 6. Dilation: Congruence and Similarity 13. Glossary and Credits 7. Product Transformation Glynlyon, Inc.

6 UNIT 11: REVIEW 1. Geometry as a System 9. Area and Volume 2. Geometry Proofs 10. Coordinate Geometry 3. Angle Relationships and Parallels 11. Quiz 3: Review: Units 7,8,10 4. Quiz 1: Review: Units Special Project* 5. Congruent Triangles and Quadrilaterals 13. Test 6. Similar Polygons 14. Alternate Test* 7. Circles 15. Glossary and Credits 8. Quiz 2: Review: Units 4,5,7 UNIT 12: SEMESTER REVIEW AND EXAM 1. Review 3. Alternate Exam - Form A* 2. Exam 4. Alternate Exam - Form B* UNIT 13: FINAL EXAM 1. Final Exam 3. Alternate Exam - Form B* 2. Alternate Exam - Form A* (*) Indicates alternate assignment Glynlyon, Inc.

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