CURRICULUM CATALOG. Geometry ( ) TX

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1 CURRICULUM CATALOG

2 Table of Contents GEOMETRY ( ) TX 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 EXAM... 2 UNIT 7: CIRCLES... 3 UNIT 8: AREA AND VOLUME... 3 UNIT 9: COORDINATE GEOMETRY... 3 UNIT 10: TRANSFORMATIONS AND TRIGONOMETRY... 3 UNIT 11: PROBABILITY... 4 UNIT 12: SEMESTER EXAM... 4 UNIT 13: FINAL EXAM Glynlyon, Inc. i

3 Course Overview is a full-year, high school credit course that is intended 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. Upon successfully completing the course, the student should have mastered the following concepts: 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. 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. Determine the equation of a line or circle. Make geometric constructions on paper. Represent results of motion geometry (translation, rotation, reflection, dilation). 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. Calculate simple probabilities using addition, multiplication, permutations, combinations, and frequency tables. Unit 1: Introduction 1. Course Overview 8. Review of Algebraic Postulates 2. : Undefined Terms: Point 9. Geometric Theorems 3. : Undefined Terms: Line 10. Review of Properties of Algebra 4. : Undefined Terms: Plane 11. Quiz 2: Postulates and Theorems 5. Defined Terms: Definitions 12. Special Project* 6. Quiz 1: Undefined and Defined Terms 13. Test 7. Geometric Postulates 14. Alternate Test* Unit 2: Logic 1. Logic 10. Using Deductive Reasoning 2. Conjunctions 11. Proof Formats: Statement of the Theorem 3. Disjunctions 12. Proof Formats: The Figure 4. Negation 13. Proof Formats: The Plan of the Proof 5. Conditional or Implication Statements 14. Indirect Proof Format: The Paragraph Proof 6. Converse, Inverse, Contrapositive 15. Quiz 2: Inductive and Deductive Reasoning 7. Inductive Reasoning 16. Special Project* 8. Quiz 1: Principles of Logic 17. Test 9. Deductive Reasoning 18. Alternate Test* 2018 Glynlyon, Inc. 1

4 Unit 3: Angles And Parallels 1. Angle Definitions 13. Continued Proofs: Transversals and Special Angles 2. Angle Measurement 14. More Proofs for Postulates 9 and Angle Relationship Definitions 15. Construction: Perpendiculars 4. Quiz 1: Angles 16. Construction: Parallels 5. Angle Relationship Theorems (1) 17. Exterior and Remote Interior Angles of a Triangle 6. Angle Relationship Theorems (2) 18. Proofs Involving Triangles 7. Construction: Copying Figures 19. Other Polygons 8. Construction: Bisecting Figures 20. Quiz 3: Triangles, Polygons, and Angle Properties 9. Basic Properties of Parallels 21. Special Project* 10. Transversals and Special Angles 22. Test 11 Quiz 2: Parallels and Transversals 23. Alternate Test* 12. More Proofs: Transversals and Special Angles Unit 4: Congruent Triangles And Quadrilaterals 1. Defining Congruent Triangles 15. Quiz 2: Types of Triangles 2. Proving Triangles Congruent (1) 16. Inequality Theorem in Two Triangles 3. Proving Triangles Congruent (2) 17. Quadrilateral Parallelograms Theorems Part 1 4. Proving Triangles Congruent (3) 18. Triangles that Use Parallelograms in Proofs 5. Quiz 1: Congruent Triangles 19. Parallelograms: Rectangles 6. Proving Right Triangles Congruent 20. Parallelograms: Rhombus 7. Independent Triangles (1) 21. Trapezoids-Definitions and Proofs 8. Independent Triangles (2) 22. Quiz 3: Parallelograms and Trapezoids 9. Overlapping Triangles (1) 23. Performance Task 10. Overlapping Triangles (2) 24. Alternate Performance Task* 11. Isosceles Triangles (1) 25. Special Project* 12. Isosceles Triangles (2) 26. Test 13. Inequality Theorem in One Triangle Part Alternate Test* 14. Inequality Theorem in One Triangle Part 2 Unit 5: Similar Polygons 1. Algebra and Ratios 12. Using Similar Triangles in Indirect Measure 2. Algebra Properties and Proportions 13. The Pythagorean Theorem 3. Quiz 1: Proportions 14. Theorem about Right Triangles 4. Properties of Proportions 15. Theorem about Right Triangles 5. Meaning of Similarity 16. Using Triangles: Rectangular Solids 6. Meaning of Similarity-Theorems 17. Using Triangles: Regular Square Pyramid 7. Meaning of Similarity-Proofs 18. Quiz 3: Similarity and Triangle Theorems 8. Theorems-Similar Polygons 19. Special Project* 9. Theorems-Special Segments in Triangles 20. Test 10. Quiz 2: Similarity 21. Alternate Test* 11. Similar Right Triangles Unit 6: Semester Exam 1. Semester Exam 2. Alternate Semester Exam* 2018 Glynlyon, Inc. 2

5 Unit 7: Circles 1. Characteristics of Circles 10. Special Angles Type 1 2. Characteristics of Spheres 11. Special Angles Type 2 3. Quiz 1: Circles, Spheres, and Non-Euclidean 12. Special Angles Type 3 4. Tangents 13. Special Segments 5. Arcs 14. Quiz 3: Special Angles and Segments 6. Chords 15. Performance Task 7. Theorems (1) 16. Alternate Performance Task* 8. Theorems (2) 17. Special Project* 9. Quiz 2: Tangents, Arcs, and Chords 18. Test 19. Alternate Test* Unit 8: Area and Volume 1. Area Concepts of Polygons 13. Solids: Pyramids 2. Area of Rectangles 14. Solids: Cylinders 3. Area of Parallelograms 15. Solids: Cones 4. Area of Triangles and Rhombuses 16. Solids: Spheres 5. Area of Trapezoids 17. Project: Rotating a Two-Dimensional Shape 6. Area of Regular Polygons 18. Two- and Three-Dimensional Shapes 7. Area Comparisons of Polygons 19. Quiz 2: Surface Area and Volume 8. Circles: Circumference and Pi 20. Performance Task 9. Quiz 1: Area of Polygons 21. Alternate Performance Task* 10. Circles: Area of Circles 22. Special Project* 11. Circles: Area of Sectors 23. Test 12. Solids: Prisms 24. Alternate Test* Unit 9: Coordinate 1. Ordered Pairs: Points in a Plane 11. Symmetry 2. Distance Formula 12. Figures in the Coordinate Plane 3. Perimeter and Area 13. Proofs with Coordinate (1) 4. Equation of a Circle 14. Proofs with Coordinate (2) 5. Quiz 1: Distance Formula and Applications 15. Quiz 3: Figures and Proofs 6. Midpoint Formula 16. Performance Task 7. Slope 17. Alternate Performance Task* 8. Parallel and Perpendicular Lines 18. Special Project* 9. Equations of Lines 19. Test 10. Quiz 2: Slope and Lines 20. Alternate Test* Unit 10: Transformations And Trigonometry 1. Introduction: Rigid Motion, or Isometry 11. Alternate Performance Task* 2. Isometry: Reflection 12. Using SOH CAH TOA in Trigonometry 3. Isometry: Translation 13. Finding the Values of Trigonometric Functions 4. Quiz 1: Isometry 14. Using Trigonometry in Indirect Measure 5. Isometry: Rotation 15. The Unit Circle 6. Transformation Sequences 16. Radian Measure 7. Similarity Transformation: Dilation 17. Quiz 3: Trigonometry 8. Product Transformation 18. Special Project* 9. Quiz 2: Transformations 19. Test 10. Performance Task 20. Alternate Test* 2018 Glynlyon, Inc. 3

6 Unit 11: Probability 1. Definitions, Sample Spaces, and Probability 9. Conditional Probability 2. Addition of Probabilities 10. Conditional Probability in Real-World Situations 3. Multiplication of Probabilities 11. Geometric Probability 4. Definitions 12. Quiz 2: Probability 5. Quiz 1: Using Probability 13. Special Project* 6. Permutations of N Things: Different 14. Test 7. Permutations of N Things: Not All Different 15. Alternate Test* 8. Combinations Unit 12: Semester Exam 1. Semester Exam 2. Alternate Semester Exam* Unit 13: Final Exam 1. Final Exam 2. Alternate Final Exam* * indicates alternative assignment 2018 Glynlyon, Inc. 4

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