Author Archives: hangtime
These videos cover everything you could want to know about chords of circles, from solving for missing angles to doing proofs about equidistant chords.
Inscribed Angle Proofs
In this video I work a few proofs, including proving Case 1 of the inscribed angle theorem which shows that inscribed angles are half the measure of the central angle.
Inscribed Angles
This video explains the theorems and corollaries involved with inscribed angles, as well as how to solve for missing angles in a circle whether they're inscribed angles, central angles, or arcs. Also covered is a common example: crisscrossing triangles (formed from intersecting chords) which are always similar.
Arcs & Central Angles
In geometry, arcs aren't measured by inches and meters, they're measured by the central angle which includes that arc. What's a central angle? What's a major and minor arc? Stick around and find out!
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.
Why Bikes & Cars Need Gears
This video definitely falls under the category of "only if you're interested in mechanical stuff", but it's important nonetheless because knowing how little stuff like bike gears work can be really important in other types of science and engineering, or even riding bikes.
Difficult Gear & Pulley Word Problems
This stuff is probably not in your geometry class, it's more for physics students or students in pre-cacl or trig who have really tough teachers, or for students interested in engineering type stuff. Gear ratios are explained as they pertain to bikes, cars, and we'll even learn how to tell how fast your bike is going from the pedal rotations!
Basic Circuference, Pulley & Wheel Word Problems
This video covers word problems involving only one rotating part. Could be a crank that raises water up from a well. Could be figuring the distance or velocity of a wheel given a number of rotations. If you're in geometry you may need this video, but it's mostly for students in more advanced classes, either honors geometry or algebra 2.
Circumference & Diameter
This video introduces pi, then it covers how to calculate circumference when you're given radius or diameter. It also covers those tricky problems where they give you circumference (sometimes it doesn't even have a pi in it) and expect you to solve for radius or diameter. Tricky stuff!
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.
Basic Circle Proofs
This video covers a couple of proofs that utilize the most basic aspects of circles, namely that all the radii of a circle are congruent. As usual, you'll also have to keep an eye out for theorems you already know from previous chapters, like triangles. It always comes back to triangles.
Circle Vocab
This video covers the basis of the following vocab items: radius, diameter, circumference, chord, secant, tangent, arcs (major & minor), inscribed angles, Central angles, concentric circles.
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.
Breaking A Concave Polygon Into Triangles
If you forget the n-2 formula for the sum of the internal angles of a polygon, this video covers the next best thing: breaking them into triangles. If done right, this technique is pretty easy, but it's tough to do correctly, especially if the polygon is concave.
Crazy Interior & Exterior Angle Polygon Problems
Other videos introduced interior and exterior angles separately. But this video covers the diciest problems, where you have to figure out which (or both) to use and then figure out the relevant formulas. Sometimes you're even solving for angle X!
Interior Angles of Polygons
This video covers the "n-2" formula for polygons, but that's not the one you're going to remember a year from now when you're taking admissions tests. The method you're going to remember is breaking up polygons into triangles, which if done properly is the easiest way to go.
Exterior Angles of Polygons
Even though external angles are a little weirder than interior angles, I like to teach these first because the formulas are so much simpler. First, they always add up to 360 for any polygon, no matter how many sides. And second, they're easy to find for regular polygons, which is the most common type of polygon you come across.
Regular vs Irregular
This video covers the basics of regular vs irregular polygons and tells you how to spot them. It also gets into what these terms mean for 3D shapes like prisms and pyramids.
Polygon Vocab
This video covers your basic everyday polygon vocab stuff: definition of polygon, names of polygons, concave vs convex, equilateral vs equiangular, regular vs irregular (there's also a longer video about regular vs irregular polygons on this page).