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Learn Geometry Fast

(from someone who can actually explain it)

Chris is a Stanford-educated tutor with over 10 years experience tutoring Geometry to students of all abilities, from students struggling to get from a C to a B, to go-getters trying to move an A- up to an A, to struggling students just hoping to pass. In that time he got a lot of experience learning how to explain this stuff in a way it actually makes sense to normal people. Through his videos he has helped countless students, and he can do the same for you.

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Geometry

Whether you're taking a class called "Geometry" or you're just reviewing for an entrance or exit exam, below are all the topics you may need.
  1. Geometry Basics:

  2. Midpoint Definition & Formula

    Videos covering the definition of midpoint, as well as how to find the coordinates of the midpoint of a line segment in the X-Y plane.

  3. The Number Line:
    negative numbers, addition & subtraction

    This video introduces the number line and explains how to use it to add and subtract negative numbers. It also explains how to determine if segments on the number line are congruent.

  4. The Ruler Postulate

    This video covers the Ruler Postulate, which is basically "geometry speak" for finding the distance between two points on the number line by subtracting their coordinates. Good stuff!

  5. Segment Addition Postulate

    This video covers the Segment Addition Postulate, which basically says that if you break a segment into two parts, the lengths of the two parts are going to add up to the length of the original segment. Shocking!

  6. X-Y Stuff:

  7. The X-Y Plane:
    vocab,
    plotting points,
    The Four Quadrants

    The videos in this topic introduce you to the X-Y plane (aka "rectangular coordinate system"), explain what the "origin" is, explain how to graph points, explain "the four quadrants", and tell you how to plot points.

  8. Basic X-Y Graphs:
    segments, circles
    collinear points,
    X- & Y-Intercepts

    If you're new to X-Y graphs, this is the place for you. We'll start with segments and lines without equations (for equations of lines from algebra, click here). Then we'll look at graphs of circles and rectangles, and x- and y-intercepts.

  9. Distance & Midpoint Formulas

    This chapter teaches you the formulas for finding the distance and midpoint between two points on the X-Y plane, as well as word problems using these formulas.

  10. Lines, Equations of Lines, & Linear Equations

    Slope-Intercept Form, Point-Slope Form, Standard Form, Vertical Lines, Horizontal Lines, Perpendicular Lines: in this chapter, we experience the splendor of all the different types of linear functions, and master the equations and graphing of each.

  11. Circles, Ellipses, Hyperbolas & Parabolas: The "Conics"

    In this chapter we'll emphasize the similarities and differences between the equations of these four shapes, and we'll discuss why conic sections are called that.

  12. Transformations, Reflections, Isometry & Mapping

    These videos tell you what translations, rotations, and dilations are, as well as showing you the steps to do reflect a shape or function across a line using graphical techniques.

  13. Triangles:

  14. Pythagorean Theorem

    This chapter covers the basic formula and how to use it on right triangles, as well as the most common mistake students make with it. Also included is a video about simplifying radicals, since that comes up a lot with Pythagorean.

  15. Classifying Triangles:
    acute vs obtuse, isosceles,
    scalene & equiliateral
    SAT

    This video covers all your basic triangle vocabulary, as well as that particular type of SAT question where they ask you if a triangle is "possible" with the given side lengths.

  16. 180 Rule for Triangles:
    Exterior angle theorem
    proofs

    The 180 rule is one of the most important things you'll learn in geometry, and it will haunt you forever if you don't get it down! The exterior angle theorem, on the other hand, is almost useless and you'll never see it or it's "inequality" version ever again. Yet both may be on the test.

  17. Intro to Congruence & Corresponding Parts:
    properties
    diagrams

    Once you get into the chapters of your book that cover congruent triangles, you're going to get so sick of congruent shapes that you'll be able to shoot your own video on them. But if you're just getting to congruence for the first time, these quick videos introduce the basics of congruent shapes and corresponding parts that you'll need so that you can understand what your teacher is talking about.

  18. Congruent Triangle Theorems & Proofs:
    SSS, SAS, ASA
    AAS, H-L

    The chapter with every possible combination and permutation of S's and A's except for one: SSA. What are these good for, how do we use them in proofs, and why exactly is SSA not a thing? Prepare to enter the fray of congruent triangles!

  19. CPCTC:
    theorems
    proofs

    Corresponding parts of corresponding triangles really are congruent. This isn't the first chapter that mentions corresponding parts, but this is where we'll get into how to use them in proofs.

  20. Right Triangle Congruence:
    H-L, L-L
    H-A, L-A

    Many geometry teachers don't cover all of these because they're redundant, right-triangle-only versions of all the congruence theorems you already know. The only one that every teacher covers is H-L.

  21. Isosceles & Equilateral Triangle Theorems:
    Base Angle Theorem
    Converse
    & Equilateral Corollaries

    Between the main theorem and the corollaries, you wouldn't believe how often you're going to come across this theorem throughout your academic career, from trig to physics to calculus to architecture and design. And the SAT!

  22. Medians, Midsegments, Altitudes & Centroids (of Triangles)

    The videos in this section cover a few different random topics in triangles that didn't really fit in anywhere else.

  23. Angle and Segment Bisectors

    These videos cover a couple of theorems about the bisectors of angles and segments. I'll save you the suspense: both involve things being equidistant, and result in congruent triangles.

  24. Indirect Proofs

    These are pretty confusing for everyone when you first see them, but then at some point you hopefully are given step-by-step instructions to make these easy. This is that moment for you!

  25. Triangle Inequalities & Side Lengths:
    SSS, SAS
    distance from points to lines & planes

    These videos cover a few theorems that all involve "inequalities". In previous chapters, you were always trying to prove two triangles or segments congruent. In this one, you're trying to prove things unequal, whether it's saying that one side in a particular triangle is longer than another side, or that a side in one triangle is longer than a side in another.

  26. Ratios & Proportions

    These videos introduce the aspects of ratios and proportions that you will need whether you're in Goeometry or you're about to take the SAT.

  27. Similar Polygons:
    missing sides,
    scale factors

    The videos in this chapter explain what similar polygons are, and how to solve various types of problems including: scale factors, missing sides, similar trapezoids. Also explained are which types of polygons are always similar.

  28. Similar Triangles:
    SSS & SAS theorems, geometric mean, proportional triangles

    If you need to find missing sides of similar triangles, that is mostly covered in the similar polygons chapter videos. Instead, this chapter of videos on similar triangles focuses on similarity theorems and proofs for triangles. Also covered are right triangle problems involving the "geometric mean" of various sides and the "altitude to the hypotenuse" of right triangles.

  29. Parallel Lines & Quadrilaterals:

  30. Parallel Lines & Transversals:
    corresponding angles
    alternating interior angles
    proofs

    This section covers all those problems where a couple of parallel lines are crossed by another line (the transversal) and you're then supposed to figure out all the angles, and show which ones are congruent.

  31. Parallelograms

    Theorems, problems, and proofs involving parallelograms.

  32. Rectangles, Squares, Kites & Rhombuses

    These quadrilaterals are kind of like The Beatles: most people have only heard of three of them: squares, rectangles, and rhombuses (rhombusi). Kites, on the other hand, are only covered in some geometry classes. This chapter has theorems, problems and proofs for all of them, but if your class doesn't cover kites, you probably shouldn't use those theorems on your next test.

  33. Trapezoids:
    isosceles, theorems,
    area problems,
    proofs

    Trapezoids are technically quadrilaterals with a single pair of parallel sides, but the reality is that most of the problems you'll ever see are isosceles trapezoids. So in this chapter most of the problems and proofs are about isosceles trapezoids, but we also discuss the little trick questions where teachers and test makers throw in the weird non-standard trapezoids to try and throw you off.

  34. Circles:

  35. Circle Basics:
    Circle Vocab
    Basic Circle Proofs

    The first video in this chapter covers the basis of the following vocab items: radius, diameter, circumference, chord, secant, tangent, arcs (major & minor), inscribed angles, Central angles, concentric. The second video covers some very basic proofs based on the fact that all the radii of a given circle are the same length.

  36. Circumference, Pulleys & Wheels

    The first video in this chapter covers basic circumference problems, where you need to get circumference when you know diameter or radius, or vice versa. Then there are two videos about pulleys and gears, car wheels and bike tires, how far and how fast a car is going when its tires rotate a certain speed. Finally we'll discuss what gear ratios are even for, and why your bike has 20 speeds in the first place.

  37. Central & Inscribed Angles:
    minor arcs
    major arcs
    theorems
    proofs

    These videos introduce arcs, arc length, central angles, and inscribed angles, then they go through lots of different examples involving solving for missing angles and arcs between.

  38. Chords of Circles:
    congruent chords
    equidistant chords
    ab=cd
    intersecting chords

    These videos cover everything you could want to know about chords of circles, from solving for missing angles to doing proofs about equidistant chords.

  39. Tangents of Circles:
    Internal vs External
    Proofs
    Angles Inscribed by Tangents

    Not to be confused with trig tangents, circle tangents are segments which sidle up alongside a circle and intersect it at exactly one point. This chapter covers the definition, problems and theorems, including how inscribed angle theorems apply to tangents.

  40. Formulas for Secants & Chords

    Videos covering problems where two secants meet outside a circle, and the problem asks you to calculate the length of the segments, or the angle between them.

  41. Area of Circles & Sectors

    This chapter is super-important if you're ever planning on taking the SAT or another tough standardized test. You won't see sectors too much after Geometry class, but circles and circle-ish regions, especially "shaded regions" involving circles and triangles, are favorite topics for test-makers everywhere!

  42. Circles in X-Y Coordinates

    This video covers equations of circles in X-Y coordinates. This topic isn't covered by most geometry teachers, but if it's in your class, here you go. For equations of other conics, like ellipses and parabolas, check out the Algebra 2 page.

  43. Area & Volume:

  44. Area of Rectangles and Squares
    &
    Area Unit Conversions

    Besides rectangles and squares, this chapter covers other basics of area such as how to convert units for area problems, such as from square cm to square meters (cm^2 to m^2) or square inches to square feet (in^2 to ft^2).

  45. Area of Triangles by:
    Pythagorean
    SohCahToa
    X-Y Coordinates
    Word Problems
    SAS
    Heron's Formula

    This topic includes videos covering just about every type of triangle area problem, all listed by type. Plus, a couple of videos that are going to SAVE YOUR BACON on every triangle problem you'll ever see, including on the SAT!

  46. Area of Parallelograms & Trapezoids

    Examples and word problems using parallelograms (parallelagrams sp) and trapezoids.

  47. Area of Kites & Rhombuses (Rhombi)

    Rhombuses unfortunately use the same area formula as kites -- A = ½ d1d2. "Unfortunate" because you won't remember that formula a year or even 3 months from now when you need it on a big test! So in this chapter, whenever I work an area problem I'll also show you how to work it using parallelograms or triangles, since that's how you'll remember to do it long after the diagonals formula is lone gone from your mind.

  48. Apothems & Area of Regular Polygons

    The first video in this chapter covers what an apothem is and how to find it. The second shows you how to use the apothem formula to find the area of regular polygons such as pentagons, hexagons, octagons, etc., and it also explains how to find the area of regular polygons a better way.

  49. Area of Circles & Sectors

    This chapter is super-important if you're ever planning on taking the SAT or another tough standardized test. You won't see sectors too much after Geometry class, but circles and circle-ish regions, especially "shaded regions" involving circles and triangles, are favorite topics for test-makers everywhere!

  50. Area & Volume of Similar Figures

    This chapter covers a particular type of problem, where they give you two similar 2-D or 3-D objects -- triangles or polygons or circles or squares or cylinders -- and expect you to figure out the scale factor, area, surface area and volume of one based on the other.

  51. Volume of 3-D Solids:
    Prisms, Cylinders, Spheres,
    Cones & Pyramids, Word Problems

    This chapter covers regular problems and word problems for how to find the volume of every type of solid: pyramids and cones, oblique and right prisms, spheres, and cylinders. Lots of word problems too, including unit conversions for units of volume: cubic inches, cubic meters, liters, etc.

  52. Surface Area of 3-D Solids:
    Prisms
    Cylinders
    Spheres
    Cones & Pyramids
    Word Problems

    These videos cover how to find the surface area of every type of solid: pyramids and cones, oblique and right prisms, spheres, and cylinders. Lots of word problems too.

  53. Trig, SohCahToa, & "Special" Triangles:

  54. SohCahToa: Intro to Sine, Cosine & Tangent

    With this chapter we'll start trig off on the right foot -- triangles -- which has worked great for my tutoring students over the years. Also covered: what SohCahToa is; what opposite, adjacent, and hypotenuse mean; how to find sine, cosine and tangent; and how to work a bunch of "solving triangles" problems.

  55. Intro to Special Triangles

    In this chapter we'll get into the 30-60-90 and 45-45-90 triangles, with special emphasis on how to find their sides, do SohCahToa on them, and not get confused between which is which. Also, some super-tricky examples for students with tough teachers.

  56. Random Topics:

  57. Geometric Probability

    This topic covers those problems where they give you a couple shapes, or a shaded region, or a shape inside another shape, or a shape next to a shape with a shaded region in between, and then you're supposed to figure out the probability that a random event (like impact by a bug or lawn dart) will strike one region or the other.

  58. Polygons:
    Regular vs Irregular
    Convex vs Concave
    Interior & Exterior Angles

    This chapter first defines everything you'd need to know about polygons: definition of polygon, names of polygons, concave vs convex, equilateral vs equiangular, regular vs irregular. Then it gets into the various types of problems you'll see, like finding interior and exterior angles, apothems of polygons, and area of polygons.

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