## Geometry

1. 1

### Euclid as the Father of Geometry

261,174 views

Euclid and his Elements (and how much Abraham Lincoln liked them)

2. 2

### Language and Notation of Basic Geometry

172,145 views

Understanding basic ideas in geometry and how we represent them with symbols

3. 3

### Lines, Line Segments, and Rays

304,428 views

Difference between lines, line segments, and rays

4. 4

### Language and Notation of the Circle

126,422 views

Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs

5. 5

### Angle Basics

226,187 views

Definition of an angle. How to denote an angle using points on the angle (including the vertex)

6. 6

### Measuring Angles in Degrees

142,393 views

How to measure an angle in degrees

7. 7

97,954 views

8. 8

### Measuring Angles

121,335 views

Using the KA virtual protractor to measure angles

9. 9

### Complementary and Supplementary Angles

148,348 views

Basics of complementary, supplementary, adjacent and straight angles. Also touching on what it means to be perpendicular

10. 10

### Angles at the intersection of two lines

82,475 views

Figuring out angles at the intersection of two lines

11. 11

### Proof-Vertical Angles are Equal

73,723 views

Proving that vertical angles are equal

12. 12

### Angles Formed by Parallel Lines and Transversals

120,660 views

Parallel lines, transversal lines, corresponding angles

13. 13

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

94,723 views

Proof that the sum of the measures of the angles in a triangle are 180

14. 14

### Triangle Angle Example 1

96,884 views

Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

15. 15

### Triangle Angle Example 2

52,387 views

Another example finding angles in triangles

16. 16

### Triangle Angle Example 3

44,679 views

Multiple ways to solve for the angles of multiple triangles

17. 17

### Challenging Triangle Angle Problem

41,221 views

Interesting problem finding the sums of particular exterior angles of an irregular pentagon

18. 18

### Proof - Corresponding Angle Equivalence Implies Parallel Lines

46,066 views

Proof by contradiction that corresponding angle equivalence implies parallel lines

19. 19

### Finding more angles

43,285 views

Example of angle hunting!

20. 20

### Sum of Interior Angles of a Polygon

104,235 views

Showing a generalized way to find the sum of the interior angles of any polygon

21. 21

### Congruent Triangles and SSS

124,640 views

What it means for triangles to be congruent

22. 22

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

39,733 views

More on the difference between a theorem and axiom. Proving a cool result using SSS

23. 23

### Other Triangle Congruence Postulates

59,892 views

SSS, SAS, ASA and AAS postulates for congruent triangles. Showing AAA is only good for similarity and SSA is good for neither

24. 24

### Two column proof showing segments are perpendicular

48,419 views

Using triangle congruency postulates to show that two intersecting segments are perpendicular

25. 25

### Sum of the exterior angles of convex polygon

44,769 views

More elegant way to find the sum of the exterior angles of a convex polygon

26. 26

### Finding Congruent Triangles

50,783 views

Using the SSS, ASA, SAS, and AAS postulates to find congruent triangles

27. 27

### More on why SSA is not a postulate

38,921 views

SSA special cases including RSH

28. 28

### Congruent Triangle Proof Example

48,390 views

Proving that a point is the midpoint via triangle congruency

29. 29

### Congruent Triangle Example 2

30,267 views

Showing that segments have the same length

30. 30

### Congruent legs and base angles of Isosceles Triangles

55,659 views

Showing that congruent legs imply equal base angles and vice versa

31. 31

### Equilateral Triangle Sides and Angles Congruent

29,011 views

Showing that all of the angles of an equilateral triangle are 60 degrees

32. 32

### Equilateral and Isosceles Example Problems

28,701 views

Three example problems involving isosceles and equilateral triangles. 2 from Art of Problem Solving (by Richard Ruscyk) book

33. 33

### Another Isosceles Example Problem

19,272 views

Possible angles for an isosceles triangle

34. 34

### Example involving an isosceles triangle and parallel lines

18,518 views

Integrating what we know about isosceles triangles and parallel lines

35. 35

### Figuring out all the angles for congruent triangles example

20,395 views

Another example of using congruency to figure out a bunch of angles

36. 36

### Perimeter and Area Basics

284,522 views

Definitions of perimeter and area.

37. 37

### Triangle Area Proofs

85,655 views

Proving that the area of any triangle is 1/2 b x h

38. 38

### Interesting Perimeter and Area Problems

54,011 views

Three example problems involving perimeter and area

39. 39

### Koch Snowflake Fractal

83,213 views

A shape that has an infinite perimeter but finite area

40. 40

### Area of an Equilateral Triangle

59,277 views

Finding the formula for the area of an equilateral triangle with side s

41. 41

### Area of Koch Snowflake (part 1) - Advanced

22,827 views

Starting to figure out the area of a Koch Snowflake (which has an infinite perimeter)

42. 42

### Area of Koch Snowflake (part 2) - Advanced

15,204 views

Summing an infinite geometric series to finally find the finite area of a Koch Snowflake

43. 43

### Challenging Perimeter Problem

29,803 views

Perimeter of rectangle covered by 9 non-overlapping squares. From 200) American Invitational Math Exam

44. 44

### Similar Triangle Basics

67,589 views

Introduction to what it means for triangles to be similar

45. 45

### Similarity Postulates

40,418 views

Thinking about what we need to know whether two triangles are similar

46. 46

### Similar Triangle Example Problems

34,064 views

Multiple examples looking for similarity of triangles

47. 47

### Similarity Example Problems

36,686 views

Two example problems involving similarity

48. 48

### Challenging Similarity Problem

18,017 views

Interesting similarity problem where we don't have a lot of information to work with

49. 49

### Similarity example where same side plays different roles

19,649 views

The same side not corresponding to itself in two similar triangles

50. 50

### Finding Area Using Similarity and Congruence

18,786 views

Example of using similarity and congruence to find the area of a triangle

51. 51

### Pythagorean Theorem Proof Using Similarity

33,303 views

Proof of the Pythagorean Theorem using similarity

52. 52

### 30-60-90 Triangle Side Ratios Proof

50,583 views

Proving the ratios between the sides of a 30-60-90 triangle

53. 53

### 45-45-90 Triangle Side Ratios

43,587 views

Showing the ratios of the sides of a 45-45-90 triangle are 1:1:sqrt(2)

54. 54

### 30-60-90 Triangle Example Problem

31,938 views

Using what we know about 30-60-0 triangles to solve what at first seems to be a challenging problem

55. 55

### The Golden Ratio

234,411 views

An introduction to one of the most amazing ideas/numbers in mathematics

56. 56

### Introduction to angles (old)

287,932 views

What an angle is. Angles in a circle. Complementary and supplementary angles.

57. 57

### Angles (part 2)

160,142 views

More on complementary and supplementary angles. Introduction to opposite angles.

58. 58

### Angles (part 3)

114,919 views

Angles formed when a transversal intersects parallel lines.

59. 59

### Angles formed between transversals and parallel lines

94,008 views

Angles of parallel lines

60. 60

### Angles of parallel lines 2

71,514 views

Angles of parallel lines examples

61. 61

### The Angle Game

154,450 views

Using what we know to solve for angles in the Angle Game.

62. 62

### Similar triangles

160,401 views

Introduction to similar triangles

63. 63

### Similar triangles (part 2)

77,071 views

More on similar triangles

64. 64

### Angle Game (part 2)

71,585 views

More examples of the Angle Game.

65. 65

### Acute Right and Obtuse Angles

115,472 views

The difference between acute, obtuse and right angles

66. 66

### Area and Perimeter

335,454 views

Area of rectangles and triangles. Perimeter of rectangles.

67. 67

### Circles: Radius, Diameter and Circumference

442,968 views

Understanding the relationship between the radius diameter and circumference of a circle.

68. 68

### Area of a circle

118,675 views

Area of a circle and how it relates to radius and diameter

69. 69

### The Pythagorean Theorem

271,935 views

Introduction to the Pythagorean Theorem

70. 70

### Pythagorean Theorem II

108,586 views

More Pythagorean Theorem examples. Introduction to 45-45-90 triangles.

71. 71

### 45-45-90 Triangles

131,287 views

Introduction to 45-45-90 Triangles

72. 72

### Intro to 30-60-90 Triangles

137,842 views

A few more 45-45-90 examples and an introduction to 30-60-90 triangles.

73. 73

### 30-60-90 Triangles II

80,748 views

More examples using 30-60-90 triangles.

74. 74

### Solid Geometry Volume

165,058 views

Volume of triangular prisms and cubes

75. 75

### Cylinder Volume and Surface Area

225,132 views

Finding the volume and surface area of a cylinder

76. 76

### Heron's Formula

102,759 views

Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides

77. 77

### Part 1 of Proof of Heron's Formula

53,063 views

Part 1 of the proof of Heron's Formula

78. 78

### Part 2 of the Proof of Heron's Formula

40,254 views

Showing that the expression in part 1 is identical to Heron's Formula

79. 79

### Inscribed and Central Angles

116,155 views

Showing that an inscribed angle is half of a central angle that subtends the same arc

80. 80

### Area of Inscribed Equilateral Triangle (some basic trig used)

66,326 views

Problem that requires us to figure out the area of an equilateral triangle inscribed in a circle (A little trigonometry used)

81. 81

### Right Triangles Inscribed in Circles (Proof)

78,865 views

Proof showing that a triangle inscribed in a circle having a diameter as one side is a right triangle

82. 82

### Area of Diagonal Generated Triangles of Rectangle are Equal

34,881 views

Area of Diagonal Generated Triangles of Rectangle are Equal

83. 83

### Triangle Medians and Centroids

44,046 views

Seeing that the centroid is 2/3 of the way along every median

84. 84

### Triangle Medians and Centroids (2D Proof)

21,063 views

Showing that the centroid is 2/3 of the way along a median

85. 85

### Rhombus Diagonals

33,662 views

Proof that the diagonals of a rhombus are perpendicular bisectors of each other

86. 86

### 2003 AIME II Problem 7

20,356 views

Area of rhombus from circumradii of triangles

87. 87

47,957 views

Simple proof using RSH postulate to show that a radius perpendicular to a chord bisects it

88. 88

### Circumcenter of a Triangle

48,987 views

Multiple proofs showing that a point is on a perpendicular bisector of a segment if and only if it is equidistant from the endpoints. Using this to establish the circumcenter, circumradius, and circumcircle for a triangle

89. 89

### Circumcenter of a Right Triangle

19,351 views

Showing that the midpoint of the hypotenuse is the circumcenter

90. 90

### Three Points Defining a Circle

33,460 views

Showing that three points uniquely define a circle and that the center of a circle is the circumcenter for any triangle that the circle is circumscribed about

91. 91

### Point Line Distance and Angle Bisectors

30,673 views

Thinking about the distance between a point and a line. Proof that a point on an angle bisector is equidistant to the sides of the angle and a point equidistant to the sides is on an angle bisector

92. 92

### Incenter and incircles of a triangle

26,802 views

Using angle bisectors to find the incenter and incircle of a triangle

93. 93

### Angle Bisector Theorem Proof

33,819 views

What the angle bisector theorem is and its proof

94. 94

16,729 views

Showing that area is equal to inradius times semiperimeter

95. 95

### Angle Bisector Theorem Examples

27,353 views

Using the angle bisector theorem to solve for sides of a triangle

96. 96

### Medians divide into smaller triangles of equal area

13,879 views

Showing that the three medians of a triangle divide it into six smaller triangles of equal area. Brief discussion of the centroid as well

97. 97

### Exploring Medial Triangles

9,718 views

What a medial triangle is and its properties

98. 98

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

12,850 views

Showing that the centroid divides each median into segments with a 2:1 ratio (or that the centroid is 2/3 along the median)

99. 99

### Median Centroid Right Triangle Example

12,783 views

Example involving properties of medians

100. 100

### Proof - Triangle Altitudes are Concurrent (Orthocenter)

22,014 views

Showing that any triangle can be the medial triangle for some larger triangle. Using this to show that the altitudes of a triangle are concurrent (at the orthocenter).

101. 101

### Review of Triangle Properties

19,262 views

Comparing perpendicular bisectors to angle bisectors to medians to altitudes

102. 102

### Euler Line

20,680 views

The magic and mystery of the Euler Line

103. 103

### Euler's Line Proof

14,815 views

Proving the somewhat mystical result that the circumcenter, centroid and orthocenter

104. 104

105. 105

### Common Orthocenter and Centroid

13,743 views

Showing that a triangle with the same point as the orthocenter and centroid is equilateral

106. 106

104,066 views

Basics of quadrilaterals including concave, convex ones. Parallelograms, rectangles, rhombi and squares

107. 107

### Proof - Opposite Sides of Parallelogram Congruent

34,994 views

Proving that a figure is a parallelogram if and only if opposite sides are congruent

108. 108

### Proof - Diagonals of a Parallelogram Bisect Each Other

37,594 views

Proving that a quadrilateral is a parallelogram if and only if its diagonals bisect each other

109. 109

### Proof - Opposite Angles of Parallelogram Congruent

30,305 views

Showing that opposite angles of a parallelogram are congruent

110. 110

### Proof - Rhombus Diagonals are Perpendicular Bisectors

28,567 views

Proving that the diagonals of a rhombus are perpendicular

111. 111

### Proof - Rhombus Area Half Product of Diagonal Length

17,241 views

Showing that we can find the area of a rhombus by taking half the product of the lengths of the diagonals

112. 112

### Area of a Parallelogram

89,720 views

Showing that the area of a parallelogram is base times height

113. 113

### Problem involving angle derived from square and circle

10,160 views

Challenging problem to find an angle

114. 114

46,858 views