Author Archives: hangtime
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!
Full Proof Examples--SSS, SAS, ASA, AAS, SSA, H-L
To keep things simple, in the previous video we "planned" a bunch of proofs. In this video we follow through on those plans, working out each proof in excruciating detail. Good times.
Triangle Proof How-To
The thing that makes triangle proofs so hard is that there are two levels: somehow you're supposed to learn to "plan" them while simultaneously dotting every i, crossing every t, and worrying about ever little theorem along the way. So in this video we skip the minutia and just talk about the plan for each proof. Then in the next video we'll do the step-by-step part.
Why SSA (or ASS) Doesn't Work
This video is short, but it's good for a few laughs (at least from me), and more importantly it answers a question that every student should know because your teacher will expect you to know it. Hint: the ambiguous case.
SSS, SAS, ASA, AAS, SSA, H-L
This video is long because it introduces and explains all of the three-letter triangle theorems. The only question this video doesn't answer: why is geometry so obsessed with congruent triangles. Je ne sais quoi.
Tips & Tricks For Congruent Triangle Proofs
This video gives you a couple of the common tricks that seem to keep popping up in proofs again and again, to jog your memory when you're having trouble with a proof. The biggies: the reflexive property of congruence, and vertical angles.
Everything You Need To Know About Congruent Triangles
Okay, not everything. More like the basics, the nuts and bolts, that form the foundation of all the theorems to come: what does congruent mean, what are corresponding parts, how am I supposed to draw those little congruency mark hashtag things on sides and angles, etc.
Definition of Corresponding Parts
This video introduces the concept of corresponding parts: what are they and what are they good for. This will end up being a really important concept in triangle proofs when we get into "CPCTC." What does that stand for? You don't want to know (but could find out with a quick search in the search bar above).
What Are Congruent Shapes
This video introduces all the nitty gritty of congruent shapes like: what are they, what are they not, does size matter, does orientation matter, mirroring, etc. Basic stuff but good stuff.
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.
180 Rule & Exterior Angle Theorem Proofs
Proofs are so awesome. In this video we prove the Triangle Exterior Angle Theorem, which is probably on your homework assignment.
Triangle Exterior Angle Theorem
This is one of those things you have to learn "just because". You won't see it again, you may not even see it on the test, yet it will be on your homework and you'll waste time studying it because you think it might be on the test. Oh well, at least you can do these problems with the 180 rule instead!
180 Triangle Rule Problems
The 180 rule sounds simple: the angles of a triangle always add up to 180 degrees. And it is simple, until they start throwing in x's, and 2x's, and 180-2x's... You get the idea.
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.
Triangle Side Length Questions (SAT)
This is a type of problem that I didn't know what to call or where to put, yet it shows up in every geometry book and (most importantly) standardized tests. It's the problem type where they give you three numbers -- say 3,4,9 -- and ask you if those could be the sides of a triangle. Not sure why those particular three numbers don't work?
Scalene, Isosceles, and Equilateral Triangles
This video covers the vocab above, and it also shows you a few of the key thoughts that should go through your mind every time you see an equilateral or isosceles triangle. "Congruent right triangles" anyone?
Obtuse, Acute, and Right Triangles
This video covers the vocab of how to name triangles based on the length of the sides.
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.
Parallel Line & Transversal Proofs
This video shows you how to use vertical angles and alternating interior angles to prove alternating exterior angles are congruent, among other things. Aren't you glad that Geometry exists to make you prove stuff that you never cared about in the first place?