Course: Geometry Dnatube
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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
