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

Law of Syllogism

  The law of syllogism basically states that if statement P= statement Q, and statement Q= statement R, then statement P= statement R. A syllogism is set up in an "if" and "then" format. For example:
                    "If the sky is dark, then it might storm"
The "if" portion of the statement is the hypothesis, and the "then" portion contains the conclusion.
                    "If the sky is dark" is the hypothesis.
                    "then it might storm" is the conclusion.
An example of a syllogism is:
                    "If it is time for lunch, then I will go to the cafeteria."
                    "If I go to the cafeteria, then I will eat."
                    "If it is time for lunch, then I will eat."

How Many Handshakes?

  For class, we were to find how many handshakes our group of 4 could do between ourselves. In order to find the number of handshakes total, we made small dot diagrams, similar to the one above, and we connected each dot in every way possible. Our solution, was that 4 people could do a maximum of 6 handshakes. In order to find the exact number of handshakes any group of any size could have, we had to find the function rule. For every rectangular function, the rule is n(n+1)÷2. So, we plugged in the number of people for "n" and got out the appropriate number of handshakes.

Desmos House

This is my Desmos house. The acute angles I noticed first were both ends of the roof. The obtuse angle, was the small space between the roof and the chimney closest to the top. The right angles include the windows, and the doorframe. the biggest challenge when it came to creating my Desmos house, was trying to figure out how to make a diagonal line for my roof. I eventually learned how to make one, thanks to Hunter.

Why Math?

  Math is used for personal, practical, and spiritual use. Personal uses include paying rent, giving tips, measuring certain household items, and baking. Practical things involving math include measuring building supplies, and measuring medication for patients. Math is used in biblical times, when Noah was building the ark, and had to use certain measuring requirements that God gave him. One doorway that impacts my daily life the most, is the personal aspects to math. I give the delivery man the right amount in tip money, and I measure things when I bake things from scratch. The verse Exodus 35:30- 36:2 stands out to me the most because it tells us to create using our God given talents. Practical spiritual windows are referred to in this verse. The practical aspect in this verse, is the creating of things, and spirituality comes in because of the biblical reference.

Hello World!

  Hello, my name is Madison. Right now the tree most important things to me are family, friends, and volleyball. This year, I'm looking forward to finding certain shape volumes and areas. I'm anxious about doing things with fractions, seeing that they have never been my strongest area in math. One thing that you might know about me, is that I enjoy alternative music and 80's music. I really like the bands Coldplay, Paramore, and Fall Out Boy.

Page 70 Questions

Page 70 #1:

  The difference between complementary and supplementary angles, is the fact that when 2 angles are complementary, their measurements will always add up to 90 degrees. When 2 angles are supplementary, their measurements will always add up to 180 degrees.
  I will remember the difference between the two, because this lesson clicked for me. I don't need any special way to depict the two, complementary means 90 to me, and supplementary means 180 to me.
  I learned that 2 angles that share the same complementary angle, are congruent. <4 + <5= 90 and
<5 + <6= 90. So <4 is congruent to <6.