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Common Orthocenter and Centroid

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Uploaded on Oct 25, 2011

Showing that a triangle with the same point as the orthocenter and centroid is equilateral
More free lessons at: http://www.khanacademy.org/video?v=pD...

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Geometry

  1. 1

    Euclid as the Father of Geometry

  2. 2

    Language and Notation of Basic Geometry

  3. 3

    Lines, Line Segments, and Rays

  4. 4

    Language and Notation of the Circle

  5. 5

    Angle Basics

  6. 6

    Measuring Angles in Degrees

  7. 7

    Using a Protractor

  8. 8

    Measuring Angles

  9. 9

    Complementary and Supplementary Angles

  10. 10

    Angles at the intersection of two lines

  11. 11

    Proof-Vertical Angles are Equal

  12. 12

    Angles Formed by Parallel Lines and Transversals

  13. 13

    Proof - Sum of Measures of Angles in a Triangle are 180

  14. 14

    Triangle Angle Example 1

  15. 15

    Triangle Angle Example 2

  16. 16

    Triangle Angle Example 3

  17. 17

    Challenging Triangle Angle Problem

  18. 18

    Proof - Corresponding Angle Equivalence Implies Parallel Lines

  19. 19

    Finding more angles

  20. 20

    Sum of Interior Angles of a Polygon

  21. 21

    Congruent Triangles and SSS

  22. 22

    SSS to Show a Radius is Perpendicular to a Chord that it Bisects

  23. 23

    Other Triangle Congruence Postulates

  24. 24

    Two column proof showing segments are perpendicular

  25. 25

    Sum of the exterior angles of convex polygon

  26. 26

    Finding Congruent Triangles

  27. 27

    More on why SSA is not a postulate

  28. 28

    Congruent Triangle Proof Example

  29. 29

    Congruent Triangle Example 2

  30. 30

    Congruent legs and base angles of Isosceles Triangles

  31. 31

    Equilateral Triangle Sides and Angles Congruent

  32. 32

    Equilateral and Isosceles Example Problems

  33. 33

    Another Isosceles Example Problem

  34. 34

    Example involving an isosceles triangle and parallel lines

  35. 35

    Figuring out all the angles for congruent triangles example

  36. 36

    Perimeter and Area Basics

  37. 37

    Triangle Area Proofs

  38. 38

    Interesting Perimeter and Area Problems

  39. 39

    Koch Snowflake Fractal

  40. 40

    Area of an Equilateral Triangle

  41. 41

    Area of Koch Snowflake (part 1) - Advanced

  42. 42

    Area of Koch Snowflake (part 2) - Advanced

  43. 43

    Challenging Perimeter Problem

  44. 44

    Similar Triangle Basics

  45. 45

    Similarity Postulates

  46. 46

    Similar Triangle Example Problems

  47. 47

    Similarity Example Problems

  48. 48

    Challenging Similarity Problem

  49. 49

    Similarity example where same side plays different roles

  50. 50

    Finding Area Using Similarity and Congruence

  51. 51

    Pythagorean Theorem Proof Using Similarity

  52. 52

    30-60-90 Triangle Side Ratios Proof

  53. 53

    45-45-90 Triangle Side Ratios

  54. 54

    30-60-90 Triangle Example Problem

  55. 55

    The Golden Ratio

  56. 56

    Introduction to angles (old)

  57. 57

    Angles (part 2)

  58. 58

    Angles (part 3)

  59. 59

    Angles formed between transversals and parallel lines

  60. 60

    Angles of parallel lines 2

  61. 61

    The Angle Game

  62. 62

    Similar triangles

  63. 63

    Similar triangles (part 2)

  64. 64

    Angle Game (part 2)

  65. 65

    Acute Right and Obtuse Angles

  66. 66

    Area and Perimeter

  67. 67

    Circles: Radius, Diameter and Circumference

  68. 68

    Area of a circle

  69. 69

    The Pythagorean Theorem

  70. 70

    Pythagorean Theorem II

  71. 71

    45-45-90 Triangles

  72. 72

    Intro to 30-60-90 Triangles

  73. 73

    30-60-90 Triangles II

  74. 74

    Solid Geometry Volume

  75. 75

    Cylinder Volume and Surface Area

  76. 76

    Heron's Formula

  77. 77

    Part 1 of Proof of Heron's Formula

  78. 78

    Part 2 of the Proof of Heron's Formula

  79. 79

    Inscribed and Central Angles

  80. 80

    Area of Inscribed Equilateral Triangle (some basic trig used)

  81. 81

    Right Triangles Inscribed in Circles (Proof)

  82. 82

    Area of Diagonal Generated Triangles of Rectangle are Equal

  83. 83

    Triangle Medians and Centroids

  84. 84

    Triangle Medians and Centroids (2D Proof)

  85. 85

    Rhombus Diagonals

  86. 86

    2003 AIME II Problem 7

  87. 87

    Perpendicular Radius Bisects Chord

  88. 88

    Circumcenter of a Triangle

  89. 89

    Circumcenter of a Right Triangle

  90. 90

    Three Points Defining a Circle

  91. 91

    Point Line Distance and Angle Bisectors

  92. 92

    Incenter and incircles of a triangle

  93. 93

    Angle Bisector Theorem Proof

  94. 94

    Inradius Perimeter and Area

  95. 95

    Angle Bisector Theorem Examples

  96. 96

    Medians divide into smaller triangles of equal area

  97. 97

    Exploring Medial Triangles

  98. 98

    Proving that the Centroid is 2-3rds along the Median

  99. 99

    Median Centroid Right Triangle Example

  100. 100

    Proof - Triangle Altitudes are Concurrent (Orthocenter)

  101. 101

    Review of Triangle Properties

  102. 102

    Euler Line

  103. 103

    Euler's Line Proof

  104. Common Orthocenter and Centroid

  105. 105

    Quadrilateral Overview

  106. 106

    Proof - Opposite Sides of Parallelogram Congruent

  107. 107

    Proof - Diagonals of a Parallelogram Bisect Each Other

  108. 108

    Proof - Opposite Angles of Parallelogram Congruent

  109. 109

    Proof - Rhombus Diagonals are Perpendicular Bisectors

  110. 110

    Proof - Rhombus Area Half Product of Diagonal Length

  111. 111

    Area of a Parallelogram

  112. 112

    Problem involving angle derived from square and circle

  113. 113

    Area of a Regular Hexagon

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