Triangles

Triangles are a huge topic on the AMC. Do you know all the right details here to do great on the AMC?

In order to answer “yes,” you should know all of the following, without any hints or prompting:

• the four centers of a triangle, how you find them, and what they do
• a few different ways to calculate the area of a triangle
• the Law of Sines and the Law of Cosines

You should also be very comfortable using:

• the interior and exterior angles of a triangle
• the medians (and maybe even cevians) of a triangle
• a triangle’s angle bisectors (and the rules that they imply)

What to do

• If everything above was old news to you, then this section should be doable. Click “complete” below, and we’ll add all the relevant quizzes to your deck. Then, during your short daily practice, we’ll occasionally quiz you on this knowledge in a way that etch it into your memory for good.
• If some or all of this was new to you, then you should still click “complete” below, and add it to your quizzes, but I recommend against adding anything else for several days, because there’s a lot here.

Work with these new cards for several days. You might also do a bit of research to refresh (or learn for the first time) the ideas given above.

You may also find it helpful to review our AMC 8 chapter on Triangles.

Special note

Although the quizes for this section are complete and ready for your use, the explanation and walkthrough of all the Triangles principles and formulas will not be ready for some time. That’s simply because there’s so much to say, all of which can be found elsewhere with a bit of research.

I made the decision to focus on getting you all the flashcards instead of the written text, because I believe the flashcards are more valuable to you.

However, as soon as possible, I will come back here and flesh this section out for you as well so that you don’t have to do the research step.