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Chapter 5

Chapter 5. Deductive Geometry ( 推論幾何 ). Euclid. 1. Congruent Triangles ( 全等三角形 ). S.S.S. (b) A.S.A (c) S.A.S. (d) R.H.S. 2. Similar Triangles ( 相似三角形 ). Equiangular ( 角全等 ) (A.A.A. or A.A.) (b) Three sides proportional ( 三邊成比 )(3 sides prop.). 3. Isosceles triangle ( 等腰三角形 ).

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Chapter 5

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  1. Chapter 5 Deductive Geometry (推論幾何) Euclid

  2. 1. Congruent Triangles (全等三角形) • S.S.S. (b) A.S.A (c) S.A.S. (d) R.H.S

  3. 2. Similar Triangles (相似三角形) • Equiangular (角全等) (A.A.A. or A.A.) (b) Three sides proportional (三邊成比)(3 sides prop.)

  4. 3. Isosceles triangle (等腰三角形) • base ∠s, isos. • sides opp., equal ∠s

  5. 4. Special lines in triangles • angle bisector (角平分線) (b) perpendicular bisector (角平分線) (c) median (中線) (d) altitude (height) (高度)

  6. P.22 Part C (A)

  7. P.23 Part D

  8. Chapter 6 Quadrilaterals (四邊形)

  9. 1. Parallelogram Properties (平行四邊形的特徵) • opposite sides are equal (對邊相等)(opp. sides of //gram) (b) opposite angles are equal (對角相等)(opp. ∠s of //gram) (c) diagonals bisect each other (對角線互相平分)(diags. of //gram)

  10. 2. Mid-point theorem (中點定理) If AP = PB and PQ = QC, then (a) PQ//BC (b) PQ

  11. 3. Intercept theorem (截線定理) • If AB // CD // EF and AC = CE, then BD = DF. (b) If PQ //BC and AP = PB, then AQ = QC.

  12. P.26 Part C (A)

  13. P.26 Part C (B)

  14. P.27 Part D

  15. Chapter 7 3-D Solids (立體)

  16. 1. Symmetry of 3-D solids (立體的對稱) • reflectional symmetry (反射對稱) -- plane of symmetry (divides the plane into two equal parts) (b) rotational symmetry (旋轉對稱) -- axis of rotational symmetry (lets the figure repeat (重覆) n times after rotating (旋轉) 360o

  17. 2. Nets (摺紙圖樣) of 3-D figures A 3-D figure may have different nets.

  18. 3. 2-D representations (代表) of 3-D objects A 3-D object can be viewed (觀看) from top, side and front sides.

  19. 4. Angle between line / plane and plane (平面) • Angle between line and plane (b) Angle between two planes

  20. 5. Eucler’s formula For a polyhedron (多面體), F + V – E = 2 F : the number of of faces V : the number of vertices E : the number of edges Eucler

  21. P.31 Part C (A)

  22. P.31 Part C (b)

  23. P.32 Part D

  24. Chapter 8 Areas and Volumes (面積與體積)

  25. 1. Pyramid (錐體) Volume A : base area h : height

  26. 2. Cone (圓錐體) volume r : radius h : height curved surface area (彎面面積) l : slant height / edge / side (斜面高度)

  27. 3. Sphere (球體) volume r : radius surface area (表面面積)

  28. 4. Similar figures and solids (相似圖形與物體) • ratio of areas : l = corresponding side (對應邊) (b) ratio of volumes :

  29. More • frustum (截角錐體) • hemisphere (半球體) • dimension (維數 / 維度)

  30. P.35 Part C (A)

  31. P.36 Part C (B)

  32. P.36 Part D

  33. x cm 4 cm 8 cm 6 cm

  34. Chapter 9 Coordinate Geometry of Straight Lines (直線的座標幾何)

  35. 1. Distance (距離) and slope (gradient) (斜率) between two points • AB (b) slope of AB

  36. 2. Angle of inclination (傾斜角度)

  37. 3. Parallel (平行)and Perpendicular (垂直) Lines • Two lines are parallel if slope of L1 = slope of L2 (b) Two lines are perpendicular if slope of L1 x slope of L2 = -1

  38. 4. Section formula (分段 程式) • If AP : PB = r : s, then (b) If P is the mid-point (中點), then

  39. P.41 Part C (A)

  40. P.41 Part C (B)

  41. P.42 Part D

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