## Course: GeometryDnatube

#### Lec 1 - Euclid as the Father of Geometry

Euclid as the Father of Geometry Euclid and his Elements (and how much Abraham Lincoln liked them)

#### Lec 2 - Language and Notation of Basic G ...

Language and Notation of Basic Geometry Understanding basic ideas in geometry and how we represent them with symbols

#### Lec 3 - Lines, Line Segments, and Rays

Lines, Line Segments, and Rays Difference between lines, line segments, and rays

#### Lec 4 - Language and Notation of the Circle

Language and Notation of the Circle Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs

#### Lec 5 - Angle Basics

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

#### Lec 6 - Measuring Angles in Degrees

Measuring Angles in Degrees How to measure an angle in degrees

#### Lec 7 - Using a Protractor

Using a Protractor

#### Lec 8 - Measuring Angles

Measuring Angles Using the KA virtual protractor to measure angles

#### Lec 9 - Complementary and Supplementary ...

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

#### Lec 10 - Angles at the intersection of t ...

Angles at the intersection of two lines Figuring out angles at the intersection of two lines

#### Lec 11 - Proof-Vertical Angles are Equal

Proof-Vertical Angles are Equal Proving that vertical angles are equal

#### Lec 12 - Angles Formed by Parallel Lines ...

Angles Formed by Parallel Lines and Transversals Parallel lines, transversal lines, corresponding angles

#### Lec 13 - Proof - Sum of Measures of Angl ...

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

#### Lec 14 - Triangle Angle Example 1

Triangle Angle Example 1 Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

#### Lec 15 - Triangle Angle Example 2

Triangle Angle Example 2 Another example finding angles in triangles

#### Lec 16 - Triangle Angle Example 3

Triangle Angle Example 3 Multiple ways to solve for the angles of multiple triangles

#### Lec 17 - Challenging Triangle Angle Problem

Challenging Triangle Angle Problem Interesting problem finding the sums of particular exterior angles of an irregular pentagon

#### Lec 18 - Proof - Corresponding Angle Equ ...

Proof - Corresponding Angle Equivalence Implies Parallel Lines Proof by contradiction that corresponding angle equivalence implies parallel lines

#### Lec 19 - Finding more angles

Finding more angles Example of angle hunting!

#### Lec 20 - Sum of Interior Angles of a Polygon

Sum of Interior Angles of a Polygon Showing a generalized way to find the sum of the interior angles of any polygon

#### Lec 21- Congruent Triangles and SSS

Congruent Triangles and SSS What it means for triangles to be congruent

#### Lec 22 - SSS to Show a Radius is Perpend ...

SSS to Show a Radius is Perpendicular to a Chord that it Bisects More on the difference between a theorem and axiom. Proving a cool result using SSS

#### Lec 23 - Other Triangle Congruence Postu ...

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

#### Lec 24 - Two column proof showing segmen ...

Two column proof showing segments are perpendicular Using triangle congruency postulates to show that two intersecting segments are perpendicular

#### Lec 25 - Sum of the exterior angles of c ...

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

#### Lec 26 - Finding Congruent Triangles

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

#### Lec 27 - More on why SSA is not a postulate

More on why SSA is not a postulate SSA special cases including RSH

#### Lec 28 - Congruent Triangle Proof Example

Congruent Triangle Proof Example Proving that a point is the midpoint via triangle congruency

#### Lec 29 - Congruent Triangle Example 2

Congruent Triangle Example 2 Showing that segments have the same length

#### Lec 30 - Congruent legs and base angles ...

Congruent legs and base angles of Isosceles Triangles Showing that congruent legs imply equal base angles and vice versa

#### Lec 31 - Equilateral Triangle Sides and ...

Equilateral Triangle Sides and Angles Congruent Showing that all of the angles of an equilateral triangle are 60 degrees

#### Lec 32- Equilateral and Isosceles Examp ...

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

#### Lec 33 - Another Isosceles Example Problem

Another Isosceles Example Problem Possible angles for an isosceles triangle

#### Lec 34 - Example involving an isosceles ...

Example involving an isosceles triangle and parallel lines Integrating what we know about isosceles triangles and parallel lines

#### Lec 35 - Figuring out all the angles for ...

Figuring out all the angles for congruent triangles example Another example of using congruency to figure out a bunch of angles

#### Lec 36 - Perimeter and Area Basics

Perimeter and Area Basics Definitions of perimeter and area.

#### Lec 37 - Triangle Area Proofs

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

#### Lec 38 - Interesting Perimeter and Area ...

Interesting Perimeter and Area Problems Three example problems involving perimeter and area

#### Lec 39 - Koch Snowflake Fractal

Koch Snowflake Fractal A shape that has an infinite perimeter but finite area

#### Lec 40 - Area of an Equilateral Triangle

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

#### Lec 41 - Area of Koch Snowflake (part 1) ...

Area of Koch Snowflake (part 1) - Advanced Starting to figure out the area of a Koch Snowflake (which has an infinite perimeter)

#### Lec 42 - Area of Koch Snowflake (part 2) ...

Area of Koch Snowflake (part 2) - Advanced Summing an infinite geometric series to finally find the finite area of a Koch Snowflake

#### Lec 43 - Challenging Perimeter Problem

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

#### Lec 44 - Similar Triangle Basics

Similar Triangle Basics Introduction to what it means for triangles to be similar

#### Lec 45 - Similarity Postulates

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

#### Lec 46 - Similar Triangle Example Problems

Similar Triangle Example Problems Multiple examples looking for similarity of triangles

#### Lec 47 - Similarity Example Problems

Similarity Example Problems Two example problems involving similarity

#### Lec 48 - Challenging Similarity Problem

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

#### Lec 49 - Similarity example where same s ...

Similarity example where same side plays different roles The same side not corresponding to itself in two similar triangles

#### Lec 50 - Finding Area Using Similarity a ...

Finding Area Using Similarity and Congruence Example of using similarity and congruence to find the area of a triangle

#### Lec 51 - Pythagorean Theorem Proof Usin ...

Pythagorean Theorem Proof Using Similarity Proof of the Pythagorean Theorem using similarity

#### Lec 52 - 30-60-90 Triangle Side Ratios Proof

30-60-90 Triangle Side Ratios Proof Proving the ratios between the sides of a 30-60-90 triangle

#### Lec 53 - 45-45-90 Triangle Side Ratios

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

#### Lec 54 - 30-60-90 Triangle Example Problem

30-60-90 Triangle Example Problem Using what we know about 30-60-0 triangles to solve what at first seems to be a challenging problem

#### Lec 55 - The Golden Ratio

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

#### Lec 56 - Introduction to angles (old)

Introduction to angles (old) What an angle is. Angles in a circle. Complementary and supplementary angles.

#### Lec 57 - Angles (part 2)

Angles (part 2) More on complementary and supplementary angles. Introduction to opposite angles.

#### Lec 58 - Angles (part 3)

Angles (part 3) Angles formed when a transversal intersects parallel lines.

#### Lec 59 - Angles formed between transvers ...

Angles formed between transversals and parallel lines Angles of parallel lines

#### Lec 60 - Angles of parallel lines 2

Angles of parallel lines 2 Angles of parallel lines examples

#### Lec 61 - The Angle Game

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

#### Lec 62 - Similar triangles

Similar triangles Introduction to similar triangles

#### Lec 63 - Similar triangles (part 2)

Similar triangles (part 2) More on similar triangles

#### Lec 64 - Angle Game (part 2)

Angle Game (part 2) More examples of the Angle Game.

#### Lec 65 - Acute Right and Obtuse Angles

Acute Right and Obtuse Angles The difference between acute, obtuse and right angles

#### Lec 66 - Area and Perimeter

Area and Perimeter Area of rectangles and triangles. Perimeter of rectangles.

#### Lec 67 - Circles: Radius, Diameter and C ...

Circles: Radius, Diameter and Circumference Understanding the relationship between the radius diameter and circumference of a circle.

#### Lec 68 - Area of a circle

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

#### Lec 69 - The Pythagorean Theorem

The Pythagorean Theorem Introduction to the Pythagorean Theorem

#### Lec 70 - Pythagorean Theorem II

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

#### Lec 71 - 45-45-90 Triangles

45-45-90 Triangles Introduction to 45-45-90 Triangles

#### Lec 72 - Intro to 30-60-90 Triangles

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

#### Lec 73 - 30-60-90 Triangles II

30-60-90 Triangles II More examples using 30-60-90 triangles.

#### Lec 74 - Solid Geometry Volume

Solid Geometry Volume Volume of triangular prisms and cubes

#### Lec 75 - Cylinder Volume and Surface Area

Cylinder Volume and Surface Area Finding the volume and surface area of a cylinder

#### Lec 76 - Heron's Formula

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

#### Lec 77 - Part 1 of Proof of Heron's Formula

Part 1 of Proof of Heron's Formula Part 1 of the proof of Heron's Formula

#### Lec 78 - Part 2 of the Proof of Heron's ...

Part 2 of the Proof of Heron's Formula Showing that the expression in part 1 is identical to Heron's Formula

#### Lec 79 - Inscribed and Central Angles

Inscribed and Central Angles Showing that an inscribed angle is half of a central angle that subtends the same arc

#### Lec 80 - Area of Inscribed Equilateral T ...

Area of Inscribed Equilateral Triangle (some basic trig used) Problem that requires us to figure out the area of an equilateral triangle inscribed in a circle (A little trigonometry used)

#### Lec 81 - Right Triangles Inscribed in Ci ...

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

#### Lec 82 - Area of Diagonal Generated Tria ...

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

#### Lec 83 - Triangle Medians and Centroids

Triangle Medians and Centroids Seeing that the centroid is 2/3 of the way along every median

#### Lec 84 - Triangle Medians and Centroids ...

Triangle Medians and Centroids (2D Proof) Showing that the centroid is 2/3 of the way along a median

#### Lec 85 - Rhombus Diagonals

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

#### Lec 86 - 2003 AIME II Problem 7

2003 AIME II Problem 7 Area of rhombus from circumradii of triangles

#### Lec 87 - Perpendicular Radius Bisects Chord

Perpendicular Radius Bisects Chord Simple proof using RSH postulate to show that a radius perpendicular to a chord bisects it

#### Lec 88 - Circumcenter of a Triangle

Circumcenter of a Triangle 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

#### Lec 89 - Circumcenter of a Right Triangle

Circumcenter of a Right Triangle Showing that the midpoint of the hypotenuse is the circumcenter

#### Lec 90 - Three Points Defining a Circle

Three Points Defining a Circle 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

#### Lec 91 - Point Line Distance and Angle B ...

Point Line Distance and Angle Bisectors 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

#### Lec 92 - Incenter and incircles of a tri ...

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

#### Lec 93 - Angle Bisector Theorem Proof

Angle Bisector Theorem Proof What the angle bisector theorem is and its proof

#### Lec 94 - Inradius Perimeter and Area

Inradius Perimeter and Area Showing that area is equal to inradius times semiperimeter

#### Lec 95 - Angle Bisector Theorem Examples

Angle Bisector Theorem Examples Using the angle bisector theorem to solve for sides of a triangle

#### Lec 96 - Medians divide into smaller tri ...

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

#### Lec 97 - Exploring Medial Triangles

Exploring Medial Triangles What a medial triangle is and its properties

#### Lec 98 - Proving that the Centroid is 2- ...

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

#### Lec 99 - Median Centroid Right Triangle ...

Median Centroid Right Triangle Example Example involving properties of medians

#### Lec 100 - Proof - Triangle Altitudes are ...

Proof - Triangle Altitudes are Concurrent (Orthocenter) 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).

#### Lec 101 - Review of Triangle Properties

Review of Triangle Properties Comparing perpendicular bisectors to angle bisectors to medians to altitudes

#### Lec 102 - Euler Line

Euler Line The magic and mystery of the Euler Line

#### Lec 103 - Euler's Line Proof

Euler's Line Proof Proving the somewhat mystical result that the circumcenter, centroid and orthocenter

#### Lec 104 - Common Orthocenter and Centroid

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

#### Lec 105 - Quadrilateral Overview

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

#### Lec 106 - Proof - Opposite Sides of Para ...

Proof - Opposite Sides of Parallelogram Congruent Proving that a figure is a parallelogram if and only if opposite sides are congruent

#### Lec 107 - Proof - Diagonals of a Paralle ...

Proof - Diagonals of a Parallelogram Bisect Each Other Proving that a quadrilateral is a parallelogram if and only if its diagonals bisect each other

#### Lec 108 - Proof - Opposite Angles of Par ...

Proof - Opposite Angles of Parallelogram Congruent Showing that opposite angles of a parallelogram are congruent

#### Lec 109 - Proof - Rhombus Diagonals are ...

Proof - Rhombus Diagonals are Perpendicular Bisectors Proving that the diagonals of a rhombus are perpendicular

#### Lec 110 - Proof - Rhombus Area Half Prod ...

Proof - Rhombus Area Half Product of Diagonal Length Showing that we can find the area of a rhombus by taking half the product of the lengths of the diagonals

#### Lec 111 - Area of a Parallelogram

Area of a Parallelogram Showing that the area of a parallelogram is base times height

#### Lec 112 - Problem involving angle derive ...

Problem involving angle derived from square and circle Challenging problem to find an angle

#### Lec 113 - Area of a Regular Hexagon

Area of a Regular Hexagon Using what we know about triangles to find the area of a regular hexagon

#### Geometry

Source of these courses is khan
Videos on geometry. Basic understanding of Algebra I necessary. After this, you'll be ready for Trigonometry.
khan  Website: http://www.dnatube.com/school/khan

#### khan

Videos are obtained from khan
COURSE NAME: Geometry