GeomeTREE (octahedron)

A polyhedron is a solid shape with 6 plane sides. The way a polyhedron and a polygon are related, is that a polygon is made up of 3 or more sides, all connected at the endpoints with congruent vertices. A polyhedron is made of 6 or more polygons. For our geomeTREE, I made an octahedron. The shape consists of 8 triangles in 2 groups of 4 triangles each. These four triangles were formed into a pyramid shape and placed base to base with the other group of 4, also formed into a pyramid. The color palate in this shape included dark blue, light yellow, rose red, and dark green. The vertices of the ornament were where each triangle made a point with the others, bound by tape. all of the sides were intersected where the different triangles met. None of the planes were parallel; however, I found the triangles to form pyramids.

Reflection:
I worked on my own for this assignment and spent a class period and a half cutting the triangles out and trying to figure out how everything would fit, and then an additional 30 minutes of finally making the little polygons into the octahedron! I learned what a polyhedron was, and that the octahedron was not made out of octagons, but rather 8 triangles. I was challenged by the actual forming of the octahedron and how the triangles could make a 3 dimensional shape. I really enjoyed the in class time, cutting the triangles out of colorful paper, listening to the Frozen soundtrack, and talking with friends while working. If I had anything to change, it would be to make the shapes due before out test and before the weekend, though my class was the only group that faced this problem. 

 

This is my finished octahedron with my beautiful friend Ruthie in the background!

Polygons

A polygon is a plane figure that is formed by three or more segments called sides. Each side intersects exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon.

My phone is a quadrilateral

This bag is a quadrilateral with small dodecagons (shapes with 12 sides)

This is a foam sponge, also a triangle

The scarf has, like, a ton of snowflakes with even more sides

The "F" on the book is a nonagon 

My "M" room letters are dodecagons

Favorites, Improvements, and Pride

The 3 things I have learned so far are that the long side of a right triangle is called the hypotenuse, I learned complementary and supplementary angles, and how to use a compass to make an equilateral triangle.

My favorite thing from math so far is making lines and triangles using compasses, which were cut out from a cereal box.

To make this class better, I would like to listen to music when we are doing our independent note taking. Music helps me focus, and I'm used to listening to music when I do my homework, study for tests, quizzes, etc.

One thing i'm proud of is the fact that, for the first time ever, I not only have an A in math, but this class is my highest grade overall. Math isn't hard for me anymore and its a whole lot more fun!

Difference Between Parallel and Non-Parallel Lines Cut by a Transversal

  A pair of parallel lines cut by a transversal would follow and apply to the theorems. Non-Parallel lines would not have congruent angles in the same places the theorem suggests, and would not show the same results parallel segments would.

Above is an example of parallel lines cut by a transversal, following the theorems and staying consistent.

To the right is a non-parallel line pair cut by a transversal. The angles, which should be congruent or supplementary to each other, are not due to false angle measurements. Angle 1 is clearly not the same measure as angle 5, which would follow the corresponding angle postulate.

Coplanar Non-parallel lines VS Skew lines

Non-parallel lines, which are on the same plane, are different from skew lines because the fact that skew lines use 3 dimensions in order to be called 'skew'. Non-parallel lines will eventually cross each other. Skew lines, due to their dimensions, will never cross or touch.

Parallel, Perpendicular, and Skew

In class, I learned what a skew line was, and also that a perpendicular line would only be considered perpendicular if it crossed with another line and made a right angle. Before this lesson, I thought that a perpendicular line could cross in any way, make an acute, obtuse, or right angle, and still be considered perpendicular.

Linear Pairs vs Vertical Angles

  Linear Pairs are two adjacent angles whose noncommon sides are on the same line. Vertical Angles are not adjacent, and their sides are formed by 2 intersecting lines. When finding a linear point, there is a line dividing 2 separate angles, and they share the same line on one side. Vertical Angles are across from each other, and share a common vertex.

   

Linear pairs are #'s 2 and 3 or  

4 and 1

Vertical Pairs are #'s 4 and 2 or

1 and 3