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POTENTIAL SYLLABUS: GEOMETRY
Miss Hall's School



PRIMARY TEXT:

Geometry, second edition, by Harold R. Jacobs, copyright 1987.

OPTIONAL SUPPLEMENTAL TEXT:

One Mathematical Cat, Please! by Carol J.V. Fisher, copyright 1998.
This is available both as a spiral-bound softcover at the MHS bookstore, and on the web.
This text (the "CAT BOOK") is officially covered in Algebra I at Miss Hall's School. Students who have entered Miss Hall's in Geometry or beyond are strongly encouraged to read this text, on their own, to gain perspectives on the mathematical language that are incorporated into the Miss Hall's curriculum. Some instructors may choose to assign this reading throughout the first few weeks of the course as homework, and give quizzes over the material—both as a review from Algebra I for some students, and as a benefit to those students who have not yet seen this material.

There are 124 class meetings in the 2002–2003 academic year: 64 in the Fall term, and 60 in the Spring term. Geometry meets four days per week, e.g., Monday, Tuesday, Wednesday, and Friday, with 50 minutes per class.

This schedule offers an approximate syllabus that will complete the course objectives by year's end. The objectives in parentheses, e.g. (GEOM1), are more fully explained in the Course Objectives List: Geometry. Emphasis should be on these course objectives. Additional material in the text, that is not specified in the course objectives, may be covered at the discretion of the instructor, as time permits.

  1. Review of Geometry Prerequisite Test material (optional)
  2. Review of Geometry Prerequisite Test material (optional)
  3. Review of Geometry Prerequisite Test material (optional)
  4. Prerequisite Quiz (optional)

    CHAPTER 1: THE NATURE OF DEDUCTIVE REASONING (LOGIC1–LOGIC6; some supplementary material needed)
  5. 1.1 Drawing Conclusions (LOGIC2)
  6. 1.2 Conditional Statements (LOGIC4)
  7. 1.3 Equivalent Statements (LOGIC5)
  8. 1.4 Definitions
  9. 1.5 Valid and Invalid Deductions (LOGIC4)
  10. 1.6 Arguments with Two Premises (LOGIC2)
  11. 1.7 Direct Proof: Arguments with Several Premises (LOGIC2, LOGIC5)
  12. 1.8 Indirect Proof; 1.9 A Deductive System

    CHAPTER 2: POINTS, LINES, AND PLANES (GEOM1–GEOM5; some supplementary material needed)
  13. 2.1 Points, Lines, and Planes (GEOM1, GEOM2)
  14. 2.2 The Ruler Postulate
  15. 2.3 Properties of Equality
  16. 2.4 Betweenness of Points
  17. 2.5 Line Segments (LINE1)
  18. 2.6 Polygons (POLY1)

    CHAPTER 3: RAYS AND ANGLES
  19. 3.1 Rays and Angles (LINE4, ANGLE1, ANGLE2)
  20. 3.2 The Protractor Postulate (ANGLE2)
  21. 3.3 Betweenness of Rays (ANGLE3)
  22. 3.4 Complementary and Supplementary Angles (ANGLE2)
  23. 3.5 Linear Pairs and Vertical Angles (ANGLE2)
  24. 3.6 Parallel and Perpendicular Lines (LINE5)

    CHAPTER 4: CONGRUENT TRIANGLES
  25. 4.1 Triangles (TRI1)
  26. 4.2 Congruent Polygons (TRI5)
  27. 4.3 Proving Triangles Congruent (TRI5)
  28. 4.4 Proving Corresponding Parts Equal (TRI5)
  29. 4.5 The Isosceles Triangle Theorem (TRI2)
  30. 4.6 The SSS Congruence Theorem (TRI5)
  31. 4.7 Constructions (CONST2, CONST4)
  32. 4.8 More Constructions (LINE2, CONST3, CONST5)

    CHAPTER 5: INEQUALITIES
  33. 5.1 Properties of Inequality
  34. 5.2 The Exterior Angle Theorem (TRI4)
  35. 5.3 Triangle Side and Angle Inequalities (TRI6)
  36. 5.4 The Triangle Inequality Theorem (TRI7)

    CHAPTER 6: PARALLEL LINES
  37. 6.1 Proving Lines Parallel (LINE6, LINE7)
  38. 6.2 Perpendicular Lines (CONST7)
  39. 6.3 The Parallel Postulate (CONST6)
  40. 6.4 Some Consequences of the Parallel Postulate (LINE7)
  41. 6.5 More on Distance (LINE3)
  42. 6.6 The Angles of a Triangle (TRI3)
  43. 6.7 Two More Ways to Prove Triangles Congruent (TRI5)

    CHAPTER 7: QUADRILATERALS
  44. 7.1 Quadrilaterals (QUAD1)
  45. 7.2 Parallelograms (QUAD3)
  46. 7.3 Quadrilaterals that are Parallelograms (QUAD3)
  47. 7.4 Rectangles, Rhombuses, and Squares (QUAD2)
  48. 7.5 Trapezoids (QUAD1)
  49. 7.6 The Midsegment Theorem
  50. catch-up day
  51. catch-up day
  52. catch-up day
  53. catch-up day
  54. catch-up day
  55. catch-up day
  56. catch-up day
  57. catch-up day
  58. catch-up day
  59. catch-up day
  60. EXAM #1
  61. EXAM #2
  62. EXAM #3
  63. EXAM #4
  64. EXAM #5

    END OF FALL TERM

    BEGINNING OF SPRING TERM

    CHAPTER 9: AREA
  65. 9.1 Polygonal Regions and Area (AREA1)
  66. 9.2 Squares and Rectangles (AREA2)
  67. 9.3 Triangles (AREA2)
  68. 9.4 Parallelograms and Trapezoids (AREA2)
  69. 9.5 The Pythagorean Theorem (TRI9)

    CHAPTER 10: SIMILARITY (GEOM5, TRI7)
    Here, it is important that girls understand the difference between congruency and similarity; instructors may pick and choose several sections in this chapter to explore this concept.
  70. exploring similarity
  71. exploring similarity
  72. exploring similarity
  73. exploring similarity

    CHAPTER 11: THE RIGHT TRIANGLE
  74. 11.3 Isoceles and 30°-60° Right Triangles (TRI10)
  75. 11.4 The Tangent Ratio (use calculator; TRI11, incorporate TRI12)
  76. 11.5 The Sine and Cosine Ratios (use calculator; TRI11, incorporate TRI12)

    CHAPTER 12: CIRCLES
  77. 12.1 Circles, Radii, and Chords (CIRCLE1)
  78. 12.2 Tangents (CIRCLE1, CIRCLE6)
  79. 12.3 Central Angles and Arcs (CIRCLE1)
  80. 12.4 Inscribed Angles (CIRCLE5)
  81. 12.5 Secant Angles (CIRCLE1)

    CHAPTER 14: REGULAR POLYGONS AND THE CIRCLE
  82. 14.1 Regular Polygons (POLY1)
  83. 14.2 The Perimeter of a Regular Polygon (POLY2)
  84. 14.3 The Area of a Regular Polygon (POLY2)
  85. 14.4 Limits
  86. 14.5 The Circumference and Area of a Circle (AREA2, CIRCLE4, CIRCLE3)
  87. 14.6 Sectors and Arcs (CIRCLE1)

    CHAPTER 15: GEOMETRIC SOLIDS
  88. 15.1 Lines and Planes in Space (GEOM1)
  89. 15.2 Rectangular Solids (CONST1)
  90. 15.3 Prisms (AREA3)
  91. 15.4 The Volume of a Prism (AREA5)
  92. 15.5 Pyramids (AREA3)
  93. 15.6 Cylinders and Cones (AREA3, AREA4, AREA5)
  94. 15.7 Spheres (AREA3, AREA6)
  95. 15.8 Similar Solids (GEOM5)

    CHAPTER 17: COORDINATE GEOMETRY
    This chapter provides an optional review of concepts studied in Algebra I. However, be sure to review coordinate concepts, derive the equation of a circle with center (h,k) and radius r, and talk about graphing circles that are given in standard form: (x-h)² + (y-k)² = r²  (CIRCLE7)
  96. 17.1 Coordinate Systems
  97. 17.2 The Distance Formula (optional)
  98. 17.3 Slope (optional)
  99. 17.4 Parallel and Perpendicular Lines (optional)
  100. 17.5 The Midpoint Formula (optional)
  101. 17.6 Coordinate Proofs (optional)
  102. catch-up day
  103. catch-up day
  104. catch-up day
  105. catch-up day
  106. catch-up day
  107. catch-up day
  108. catch-up day
  109. catch-up day
  110. catch-up day
  111. catch-up day

    ADDITIONAL EXPLORATION (EXPL):
    8: TRANSFORMATIONS, or
    13: THE CONCURRENCE THEOREMS, or
    16: NON-EUCLIDEAN GEOMETRIES
  112. optional chapter
  113. optional chapter
  114. optional chapter
  115. optional chapter
  116. optional chapter
  117. optional chapter
  118. optional chapter
  119. optional chapter
  120. EXAM #1
  121. EXAM #2
  122. EXAM #3
  123. EXAM #4
  124. EXAM #5

    END OF SPRING TERM