Download Geometry Topics covered in The Campus School Math Program

Geometry http://www.khanacademy.org Basic understanding of Algebra I necessary. After this, you'll be ready for Trigonometry.
Green = covered in grades 4-8
Blue = not covered (needs Algebra 1 /Trig)
Red = not covered in 2 column proof form
1. Basic Language and Notation of Geometry Lines, line segments, rays and points. A little bit about dimensions
2. Lines, Line Segments, and Rays Lines, line segments, rays and points. A little bit about dimensions
3. Language and Notation of the Circle Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs
4. Angle Basics Definition of an angle. How to denote an angle using points on the angle (including the vertex)
5. Measuring Angles in Degrees How to measure an angle in degrees
6. Using a Protractor
7. Measuring Angles Using the KA virtual protractor to measure angles
8. Complementary and Supplementary Angles Basics of complementary, supplementary
9. Angles at the intersection of two lines Figuring out angles at the intersection of two lines
10. Proof-Vertical Angles are Equal Proving that vertical angles are equal
11. Angles Formed by Parallel Lines and Transversals Parallel lines, transversal lines,
12. Proof - Sum of Measures of Angles in a Triangle are 180
13. Triangle Angle Example 1 Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles
14. Triangle Angle Example 2 Another example finding angles in triangles
15. Triangle Angle Example 3 Multiple ways to solve for the angles of multiple triangles
16. Challenging Triangle Angle Problem Interesting problem finding the sums of particular exterior angles of an irregular pentagon
17. Proof - Corresponding Angle Equivalence Implies Parallel Lines Proof by contradiction that corresponding angle equivalence implies parallel lines
18. Finding more angles Example of angle hunting!
19. Sum of Interior Angles of a Polygon Showing a generalized way to find the sum of the interior
20. Congruent Triangles and SSS What it means for triangles to be congruent
21. SSS to Show a Radius is Perpendicular to a Chord that it Bisects More on the difference between a theorem
22. Other Triangle Congruence Postulates SSS, SAS, ASA and AAS postulates for congruent
23. Two column proof showing segments are perpendicular Using triangle congruency postulates to show that two intersecting segments are perpendicular
24. Sum of the exterior angles of convex polygon More elegant way to find the sum of
25. Finding Congruent Triangles Using the SSS, ASA, SAS, and AAS postulates to find congruent
26. More on why SSA is not a postulate SSA special cases including RSH
27. Congruent Triangle Proof Example Proving that a point is the midpoint via triangle congruency
28. Congruent Triangle Example 2 Showing that segments have the same length
29. Congruent legs and base angles of Isosceles Triangles Showing that congruent legs imply equal base
30. Equilateral Triangle Sides and Angles Congruent Showing that all of the angles of an equilateral triangle are 60 degrees
31. Equilateral and Isosceles Example Problems Three example problems involving isosceles and equilateral
32. Another Isosceles Example Problem Possible angles for an isosceles triangle (Algebraic)
33. Example involving an isosceles triangle and parallel lines Integrating what we know about isosceles triangles and parallel lines (Algebraic)
34. Figuring out all the angles for congruent triangles example Another example of using congruency to figure out a bunch of angles
35. Perimeter and Area Basics Definitions of perimeter and area.
36. Triangle Area Proofs Proving that the area of any triangle is 1/2 b x h
37. Interesting Perimeter and Area Problems Three example problems involving perimeter and area
38. Koch Snowflake Fractal A shape that has an infinite perimeter but finite area
39. Area of an Equilateral Triangle Finding the formula for the area of an equilateral triangle with side s
40. Area of Koch Snowflake (part 1) - Advanced Starting to figure out the area of a Koch Snowflake (which has an infinite perimeter)
41. Area of Koch Snowflake (part 2) - Advanced Summing an infinite geometric series to finally find the finite area of a Koch Snowflake
42. Challenging Perimeter Problem Perimeter of rectangle covered by 9 non-overlapping squares. From 200) American Invitational Math Exam
43. Similar Triangle Basics Introduction to what it means for triangles to be similar
44. Similarity Postulates Thinking about what we need to know whether two triangles are similar
45. Similar Triangle Example Problems Multiple examples looking for similarity of triangles
46. Similarity Example Problems Two example problems involving similarity
47. Challenging Similarity Problem Interesting similarity problem where we don't have a lot of information to work with
48. Similarity example where same side plays different roles The same side not corresponding to itself in two similar triangles
49. Finding Area Using Similarity and Congruence Example of using similarity and congruence to find the area of a triangle
50. Pythagorean Theorem Proof Using Similarity Proof of the Pythagorean Theorem using similarity
51. 30-60-90 Triangle Side Ratios Proof Proving the ratios between the sides of a 30-60-90 triangle
52. 45-45-90 Triangle Side Ratios Showing the ratios of the sides of a 45-45-90 triangle are 1:1:sqrt(2)
53. 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
54. The Golden Ratio An introduction to one of the most amazing ideas/numbers in mathematics
55. Introduction to angles (old) What an angle is. Angles in a circle. Complementary and
56. Angles (part 2) More on complementary and supplementary angles. Introduction to opposite
57. Angles (part 3) Angles formed when a transversal intersects parallel lines
58. Angles formed between transversals and parallel lines Angles of parallel lines
59. Angles of parallel lines 2 Angles of parallel lines examples
60. The Angle Game Using what we know to solve for angles in the Angle Game.
61. Similar triangles Introduction to similar triangles
62. Similar triangles (part 2) More on similar triangles
63. Angle Game (part 2) More examples of the Angle Game.
64. Acute Right and Obtuse Angles The difference between acute, obtuse and right angles
65. Area and Perimeter Area of rectangles and triangles. Perimeter of rectangles.
66. Circles: Radius, Diameter and Circumference Understanding the relationship between
67. Area of a circle Area of a circle and how it relates to radius and diameter
68. The Pythagorean Theorem Introduction to the Pythagorean Theorem
69. Pythagorean Theorem II More Pythagorean Theorem examples. Introduction to 45-45-90 triangles.
70. 45-45-90 Triangles Introduction to 45-45-90 Triangles
71. Intro to 30-60-90 Triangles A few more 45-45-90 examples and an introduction to 30-6072. 30-60-90 Triangles II More examples using 30-60-90 triangles
73. Solid Geometry Volume Volume of triangular prisms and cubes
74. Cylinder Volume and Surface Area Finding the volume and surface area of a cylinder
75. Heron's Formula Using Heron's Formula to determine the area of a triangle while only knowing
76. Part 1 of Proof of Heron's Formula Part 1 of the proof of Heron's Formula
77. Part 2 of the Proof of Heron's Formula Showing that the expression in part 1 is identical to Heron's Formula
78. Inscribed and Central Angles Showing that an inscribed angle is half of a central angle th
79. 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)
80. 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
81. Area of Diagonal Generated Triangles of Rectangle are Equal
82. Triangle Medians and Centroids Seeing that the centroid is 2/3 of the way along every median
83. Triangle Medians and Centroids (2D Proof) Showing that the centroid is 2/3 of the way along a median
84. Rhombus Diagonals Proof that the diagonals of a rhombus are perpendicular bisectors of each other
85. 2003 AIME II Problem 7 Area of rhombus from circumradii of triangles
86. Perpendicular Radius Bisects Chord Simple proof using RSH postulate to show that a radius perpendicular to a chord bisects it
87. 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
88. Circumcenter of a Right Triangle Showing that the midpoint of the hypotenuse is the circumcenter
89. 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
90. 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
91. Incenter and incircles of a triangle Using angle bisectors to find the incenter and incircle of a triangle
92. Angle Bisector Theorem Proof What the angle bisector theorem is and its proof
93. Inradius Perimeter and Area Showing that area is equal to inradius times semiperimeter
94. Angle Bisector Theorem Examples Using the angle bisector theorem to solve for sides of a triangle
95. 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
96. Exploring Medial Triangles What a medial triangle is and its properties
97. 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)
98. Median Centroid Right Triangle Example Example involving properties of medians
99. 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).
100.
Review of Triangle Properties Comparing perpendicular bisectors to angle bisectors to medians to altitudes
101.
Euler Line The magic and mystery of the Euler Line
102.
Euler's Line Proof Proving the somewhat mystical result that the circumcenter, centroid and orthocenter
103.
Common Orthocenter and Centroid Showing that a triangle with the same point as the orthocenter and centroid is equilateral
104.
Quadrilateral Overview Basics of quadrilaterals including concave, convex ones. Parallelograms, rectangles, rhombi and squares
105.
Proof - Opposite Sides of Parallelogram Congruent Proving that a figure is a parallelogram if and only if opposite sides are congruent
106.
Proof - Diagonals of a Parallelogram Bisect Each Other Proving that a quadrilateral is a parallelogram if and only if its diagonals bisect each other
107.
Proof - Opposite Angles of Parallelogram Congruent Showing that opposite angles of a parallelogram are congruent
108.
Proof - Rhombus Diagonals are Perpendicular Bisectors Proving that the diagonals of a rhombus are perpendicular
109.
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
110.
Area of a Parallelogram Showing that the area of a parallelogram is base times height
111.
Problem involving angle derived from square and circle Challenging problem to find an angle
112.
Area of a Regular Hexagon Using what we know about triangles to find the area of a regular hexagon