Inductive and Deductive Reasoning in Geometry
- Inductive and deductive reasoning is when you use something that you already know, or something that you can tell to be true to answer a question. For example, if you know that side A is equal to side B, and you know that side A is 15cm, it can be induced or deduced that side B is 15cm.
- The four points of concurrency of triangles are the orthocenter, centroid, circumcenter and incenter.
One geometry topic that I really enjoyed was discovering and proving triangle properties, especialy the section that focused on finding the measurements of the angles of a triangle. I really liked this section because there was a simple, straightforward and almost algebraic formula to find the measurements of each angle. As algebra is my favorite form of math, I really enjoyed being able to incorporate it into geometry.
"The mathematician does not study pure mathematics because it is useful; he studies it
because he delights in it and he delights in it because it is beautiful."
-J.H.Poincare
I have two reactions to this quote: the immediate one is: "WHAT!?!?! How can MATH be beautiful?!" However, even as I let it settle in my mind, it makes perfect sense, for there is a beauty and a satisfaction that comes from certain aspects of math for me. The one part of math that I enjoy most and find most beautiful is everything that involves algebraic equations, such as all of the triangle conjectures. I love that feeling where you know that you have the right answer, and feeling that generally comes only in math. To me, this feeling is satisfying, fun and beautiful. Even in math, this feeling doesn't come when you are working with general shapes, using deduction and induction, but it does come in the solving or creating of an equation, which I love.
