## Geometry

## Tessellation Project

For a math project we had to make a tessellation! This was my first draft of my rotational tessellation. I used this tessellation and colored it on a bigger piece of paper.

## Properties of Polygons

The last thing we worked on in this semester was properties of polygons. I enjoyed and understood the rules and concepts of each polygon. In this unit we applied all the concepts we have been learning in this semester together.

## "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 (1854-1912)

When I read this quote, I agreed with what the author was saying. When I am working on a problem or excited to get the answer to something that is a struggle, and I finally get the answer I was looking for, I am finally satisfied. When he says, "it delights him because it is beautiful", I think the author means he finds it elegant and fun to explore through mathematics. I think he finds it very interesting to learn things and even though math can be a struggle, he finds it beautiful when he finally gets the answer and the satisfaction of figuring something out.

## Problem Of The Week

Every week we are given a POW (problem of the week). They are challenging questions that require a lot of thinking. Out of all the problems I enjoyed, my favorite was Deductive Reasoning Logic Puzzles. Though they can be confusing and easy to mess up, I learned to work things through.

## Inductive and Deductive Reasoning

We have been learning about inductive and deductive reasoning. Inductive reasoning is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. Deductive reasoning evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily flows from a hypothesis. The difference between inductive and deductive reasoning is that inductive reasoning starts with observations of specific situations, then establishes a general rule to fit the observed facts. Deductive reasoning starts with a general rule, then applies that rule to a specific instance.

## Patterns into Equations

When we were working on this topic, we had a stream of numbers with a pattern. We would have to figure out what the pattern was, find the next couple of numbers, and then find an equation that let us solve for any term in the sequence without finding all the terms along the way. Once we had that equation, we could determine the hundredth, thousandth, or even millionth term. I found this topic challenging, but I thought it was an interesting way to think about what equations are really for.

## Special Angle Relationships

Special angle relationships are the relationships of the angles formed when a transversal cuts across a set of parallel lines. When there is a set of parallel lines and another line crosses them, there are some special relationships among the angles created. In these parallel lines with the transversal you can find adjacent angles, supplementary angles, alternate interior angles, alternate exterior angles, and corresponding angles. It makes sense that the angles would follow a pattern; because the transversal is a line, it maintains the same angle throughout. So, when you cross parallel lines with it, you create the same angles at the intersection with each one.

## Points of Concurrency of Triangles

When we worked on learning about points of concurrency in triangles, we used our graphing calculators to locate, circumcenter, incenter, and centroid of triangles. We also did constructions with a compass and straight edge of points of concurrency, congruent segments, angles, bisectors, and perpendiculars. Since there are so many constructions you can make it took us a while to remember and learn them all. Learning all the vocabulary of triangles and angles, and what the words really mean and translate to on paper, really helps you understand how triangles work.