The next link is a nice tool to help you with an Algebra review, as well as keep you on your toes on your Geometric definitions, postulates, and Theorems; this web page is a great resource to review your Geometry vocab. You can create a free account, and this will let you record your progress, or you can pay for your account and get to experience the extra features this site has to offer. In the Geometry section there are various topics to choose from; one subsection I will discuss for a bit is the Logic section, I know what does logic have to with Geometry? It is unfortunate that this important section is more often than the not omitted from our classrooms. It is important since it gives you a formal introduction to abstract math, and can be very helpful for Geometric proofs. For extra credit take the logic part, review the sections for logic and then complete the sheet I have in our class.
Wolfram is an excellent math free website to get familiar with, and Wolfram Alpha is an excellent site to purchase.Besides having cool Geometry features, it will help you out at a very high level in math, it will compute complicated integrals, Integrals are a part of Integral Calculus, it will also help you out with graphs and computations. Checkout the Geometry section, in the Geometry section y'all can check out complementary angles, circles, and polygons.
Geogebra is an awesome resource! This particular part of Geogebra is a sketch pad, it will help you to develop an understanding of the Theorems and corollaries. It is a great visual resource. In the top left corner there are the selection of shapes, curves, or roots; when you press the selection, you can drag it the the sketch pad and discover, and visually see, the properties of Theorems. Just for fun, try to negate the fifth postulate of Euclid, what did you come up with? There will be an entire link dedicated to this awesome Modern Mathematical discovery.
All about the Fifth
This section is completely dedicated to Euclid's fifth postulate, i know, I know; who cares about Euclid's fifth? Well, Euclid's fifth was a dilemma to Mathematicians, out of all of the five postulates that Euclid came up with, the fifth postulate seems more like a theorem. So, a lot of time, and energy, was dedicated to show that the Euclid's fifth was more of Theorem than a postulate. It is this inquiry that led to a beautiful section in Math, and it was defined, very creatively, as Non-Euclidean Geometry. The youtube video is just for fun, please do not overwhelm yourself and if you have any comments, questions, or concerns you can always ask me.
Very Important stuffs
There will be one question in your final exam that will be worth 25% of your final exam. The good news is that it will be a variation of showing that the sum of the triangles are 180 degrees, the bad news is that it will be a proof. The upcoming link will discuss and show you the proof for the sum of angles in a triangle being 180 degrees. Make sure to study, know it, recall it, but never memorize it. Let me know of any questions for this proofs, and if you come up with a new proof, there will be extra credit points.