Geometry - Khan Academy FREE

1) Euclid as the father of geometry | Introduction to Euclidean geometry | Geometry

We don't normally delve too far into history when talking about math, but sometimes it's important to have perspective about how some of our math concepts came about and how influential they have beco ...

2) Basic geometry: language and labels | Introduction to Euclidean geometry | Geometry

Before learning any new concept (mathematical or otherwise), it's important we learn and use a common language and label concepts consistently.

3) Intro to lines, line segments, and rays | Geometry

Let's get familiar with the difference between lines, line segments, and rays. Hint: a ray is somewhere between a line and a line segment! Practice this lesson yourself on KhanAcademy.org right now: ...

4) Language and notation of the circle | Introduction to Euclidean geometry | Geometry

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

5) Angle basics | Angles and intersecting lines | Geometry

The naming of an angle is related to the line segments that create it. We'll also learn about the angle's vertex. Come on. Let's do this.

6) Measuring angles in degrees | Angles and intersecting lines | Geometry

Let's come up with an exact way to measure an angle using a protractor. We'll also learn about acute angles. Not to be confused with augly angles :)

7) Measuring angles using a protractor | Angles and intersecting lines | Geometry

Let's use our virtual protractor to measure some angles together, shall we?

8) More angle measurements using a protractor | Angles and intersecting lines | Geometry

We're practicing measuring angles using the virtual protractor. Do this a few times with us and you'll use a real protractor like a pro! Practice this lesson yourself on KhanAcademy.org right now: ...

9) Complementary and supplementary angles | Angles and intersecting lines | Geometry

Let's add some tools to our geometry tool belt. Here's a thorough explanation of complementary and supplementary angles, as well as definitions of adjacent and straight angles. Practice this lesson y ...

10) Introduction to vertical angles | Angles and intersecting lines | Geometry

By using our knowledge of supplementary, adjacent, and vertical angles, we can solve problems involving the intersection of two lines. Including this one! Practice this lesson yourself on KhanAcademy ...

11) Proof: Vertical angles are equal | Angles and intersecting lines | Geometry

Proving that vertical angles are equal Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

12) Angles formed by parallel lines and transversals | Geometry

Parallel lines, transversal lines, corresponding angles Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

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

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

14) Triangle angle example 1 | Angles and intersecting lines | Geometry

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

15) Triangle angle example 2 | Angles and intersecting lines | Geometry

Another example finding angles in triangles

16) Triangle angle example 3 | Angles and intersecting lines | Geometry

Multiple ways to solve for the angles of multiple triangles

17) Challenging triangle angle problem | Angles and intersecting lines | Geometry

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

18) Proof: Corresponding angle equivalence implies parallel lines | Geometry

Proof by contradiction that corresponding angle equivalence implies parallel lines

19) Finding more angles | Angles and intersecting lines | Geometry

Example of angle hunting! Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

20) Sum of interior angles of a polygon | Angles and intersecting lines | Geometry

Showing a generalized way to find the sum of the interior angles of any polygon Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

21) Congruent triangles and SSS | Congruence | Geometry

What it means for triangles to be congruent

22) SSS to show a radius is perpendicular to a chord that it bisects | Geometry

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

23) Other triangle congruence postulates | Congruence | Geometry

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

24) Two column proof showing segments are perpendicular | Congruence | Geometry

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

25) Sum of the exterior angles of convex polygon | Geometry

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

26) Finding congruent triangles | Congruence | Geometry

Using the SSS, ASA, SAS, and AAS postulates to find congruent triangles Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

27) More on why SSA is not a postulate | Congruence | Geometry

SSA special cases including RSH

28) Congruent triangle proof example | Congruence | Geometry

Proving that a point is the midpoint via triangle congruency

29) Congruent triangle example 2 | Congruence | Geometry

Showing that segments have the same length

30) Congruent legs and base angles of isosceles triangles | Congruence | Geometry

Showing that congruent legs imply equal base angles and vice versa Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

31) Equilateral triangle sides and angles congruent | Congruence | Geometry

Showing that all of the angles of an equilateral triangle are 60 degrees Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

32) Equilateral and isosceles example problems | Congruence | Geometry

Three example problems involving isosceles and equilateral triangles. 2 from Art of Problem Solving (by Richard Rusczyk) book Practice this lesson yourself on KhanAcademy.org right now: https://www ...

33) Another isosceles example problem | Congruence | Geometry

Possible angles for an isosceles triangle

34) Example involving an isosceles triangle and parallel lines | Congruence | Geometry

Integrating what we know about isosceles triangles and parallel lines

35) Figuring out all the angles for congruent triangles example | Congruence | Geometry

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

36) Perimeter and area: the basics | Perimeter, area, and volume | Geometry

Great geometry primer on perimeter and area. Listen carefully. Sal explains the concepts so you'll understand them. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacade ...

37) Triangle area proofs | Perimeter, area, and volume | Geometry

Proving that the area of any triangle is 1/2 b x h Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

38) Interesting perimeter and area problems | Perimeter, area, and volume | Geometry

Three example problems involving perimeter and area

39) Koch snowflake fractal | Perimeter, area, and volume | Geometry

A shape that has an infinite perimeter but finite area

40) Area of an equilateral triangle | Perimeter, area, and volume | Geometry

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

41) Area of Koch snowflake (part 1) - advanced | Perimeter, area, and volume | Geometry

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

42) Area of Koch snowflake (part 2) - advanced | Perimeter, area, and volume | Geometry

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

43) Challenging perimeter problem | Perimeter, area, and volume | Geometry

Perimeter of rectangle covered by 9 non-overlapping squares. From 2000 American Invitational Math Exam

44) Similar triangle basics | Similarity | Geometry

Introduction to what it means for triangles to be similar Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

45) Similarity postulates | Similarity | Geometry

Thinking about what we need to know to determine whether two triangles are similar Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

46) Similar triangle example problems | Similarity | Geometry

Multiple examples looking for similarity of triangles Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

47) Similarity example problems | Similarity | Geometry

Two example problems involving similarity Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

48) Challenging similarity problem | Similarity | Geometry

Interesting similarity problem where we don't have a lot of information to work with Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

49) Similarity example where same side plays different roles | Similarity | Geometry

The same side not corresponding to itself in two similar triangles Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

50) Finding area using similarity and congruence | Similarity | Geometry

Example of using similarity and congruence to find the area of a triangle Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

51) Pythagorean theorem proof using similarity | Geometry

Proof of the Pythagorean Theorem using similarity Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

52) 30-60-90 triangle side ratios proof | Right triangles and trigonometry | Geometry

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

53) 45-45-90 triangle side ratios | Right triangles and trigonometry | Geometry

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

54) 30-60-90 triangle example problem | Right triangles and trigonometry | Geometry

Using what we know about 30-60-90 triangles to solve what at first seems to be a challenging problem Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/g ...

55) The golden ratio | Introduction to Euclidean geometry | Geometry

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

56) Introduction to angles (old) | Angles and intersecting lines | Geometry

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

57) Angles (part 2) | Angles and intersecting lines | Geometry

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

58) Angles (part 3) | Angles and intersecting lines | Geometry

Angles formed when a transversal intersects parallel lines.

59) Angles formed between transversals and parallel lines | Geometry

Angles of parallel lines

60) Angles of parallel lines 2 | Angles and intersecting lines | Geometry

Angles of parallel lines examples

61) The angle game | Angles and intersecting lines | Geometry

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

62) Similar triangles | Similarity | Geometry

Introduction to similar triangles

63) Similar triangles (part 2) | Similarity | Geometry

More on similar triangles

64) Angle game (part 2) | Angles and intersecting lines | Geometry

More examples of the Angle Game.

65) Acute right and obtuse angles | Angles and intersecting lines | Geometry

We briefly discussed the types of angles in the last tutorial but we'll delve a little deeper into acute, obtuse, and right angles here. Practice this lesson yourself on KhanAcademy.org right now: ...

66) Area and Perimeter

Area of rectangles and triangles. Perimeter of rectangles.

67) Circles: radius, diameter, circumference and Pi | Geometry

A circle is at the foundation of geometry and how its parts relate to each other is both completely logical and a wonder. Practice this lesson yourself on KhanAcademy.org right now: https://www.k ...

68) Area of a circle

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

69) The Pythagorean theorem intro | Right triangles and trigonometry | Geometry

Introduction to the Pythagorean Theorem Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

70) Pythagorean theorem II | Right triangles and trigonometry | Geometry

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

71) 45-45-90 triangles | Right triangles and trigonometry | Geometry

Introduction to 45-45-90 Triangles

72) Intro to 30-60-90 triangles | Right triangles and trigonometry | Geometry

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

73) 30-60-90 Triangles II

More examples using 30-60-90 triangles. More free lessons at: http://www.khanacademy.org/video?v=3mLUJ

74) Find the volume of a triangular prism and cube | Geometry

In this tutorial we'll practice finding solid geometry volume. Keep paper and pencil nearby in case you want to remember the formulas. Practice this lesson yourself on KhanAcademy.org right now: ...

75) Cylinder volume and surface area | Perimeter, area, and volume | Geometry

Finding the volume and surface area of a cylinder Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

76) Heron's formula | Perimeter, area, and volume | Geometry

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

77) Part 1 of proof of Heron's formula | Perimeter, area, and volume | Geometry

Part 1 of the proof of Heron's Formula

78) Part 2 of proof of Heron's formula | Perimeter, area, and volume | Geometry

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

79) Inscribed and central angles | Circles | Geometry

Showing that an inscribed angle is half of a central angle that subtends the same arc Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

80) Area of inscribed equilateral triangle (some basic trig used) | Circles | Geometry

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

81) Right Triangles Inscribed in Circles (Proof)

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

82) Area of diagonal generated triangles of rectangle are equal | Geometry

Area of Diagonal Generated Triangles of Rectangle are Equal

83) Triangle medians and centroids | Special properties and parts of triangles | Geometry

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

84) Triangle medians and centroids (2D proof) | Geometry

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

85) Rhombus diagonals | Quadrilaterals | Geometry

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

86) 2003 AIME II problem 7 | Special properties and parts of triangles | Geometry

87) Perpendicular radius bisects chord | Congruence | Geometry

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

88) Circumcenter of a triangle | Special properties and parts of triangles | Geometry

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 circum ...

89) Circumcenter of a right triangle | Geometry

Showing that the midpoint of the hypotenuse is the circumcenter

90) Three points defining a circle | Special properties and parts of triangles | Geometry

Three points uniquely define a circle. The center of a circle is the circumcenter of any triangle the circle is circumscribed about.

91) Point-line distance and angle bisectors | Geometry

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) Incenter and incircles of a triangle | Geometry

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

93) Angle bisector theorem proof | Special properties and parts of triangles | Geometry

What the angle bisector theorem is and its proof

94) Inradius, perimeter, and area | Special properties and parts of triangles | Geometry

Showing that area is equal to inradius times semiperimeter

95) Angle bisector theorem examples | Geometry

Using the angle bisector theorem to solve for sides of a triangle Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geome ...

96) Medians divide into smaller triangles of equal area | Geometry

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) Exploring medial triangles | Special properties and parts of triangles | Geometry

What a medial triangle is and its properties

98) Proving that the centroid is 2-3rds along the median | Geometry

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) Median centroid right triangle example | Geometry

Example involving properties of medians

100) Proof: Triangle altitudes are concurrent (orthocenter) | Geometry

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).