Cut By a Transversal

Parallel Lines                           Non-Parallel Lines:

        Not having parallel lines and splitting them with a transversal would throw off your data. You'd think that something would be true when it's not. You would be able to use the Theorems with regular parallel lines but when they aren't parallel you don't know what formulas to use, if any! Using parallel lines just simplify all your work. While Non-Parallel line make them more difficult than it should be.

Practice A Theorems

                                                                    Theorem 3.1:
All right angles congruent.

                                                                    Theorem 3.2:
 If two lines are perpendicular, then they intersect too form four right angles.

                                                                      Theorem 3.3:
If two lines intersect to form adjacent angles, then the lines are perpendicular.

                                                                      Theorem 3.4:
If two sides of adjacent acute angles are perpendicular, then the angles are complementary.

Linear Pair and Vertical Angles

          Linear Pairs are a group of non adjacent angles that equal up to 180 degrees. Linear Pairs lie on the same line and are split (not always in half).

          Vertical Angles are always congruent and opposite of each other. They are share a vertex and can be more or less than 180 degrees. It doesn't matter how many lines split the figure, as long as there are two or more lines intersecting then there are always Vertical Angles.

Law of Syllogism

          The Law of Syllogism is when there are two hypothesis and conclusion statements and you put them together.There is one topic with two separate statements in them, and you combine the hypothesis statement from the first sentence and the conclusion from the second sentence.
           Example:
If I'm 6'2, then I am tall,
if i am tall, then i can see over people.
So the syllogism of those statements are - If I'm 6'2, then i can see over people.

Question ! Page 70

Complementary angles equal 90 degrees and are located on the edge. While supplementary angles are located on the side and equal 180 degrees.
CA=90 degrees
SA=180 degrees
I learned that supplementary angles are located on the side and that complementary angles are located on the corner.

How Many Handshakes?

If there are 3 to 5 people in one group of people trying to handshake each other, the results may vary. With 3 people in one group you can have 3 handshakes. With 4 people you can can have  6 handshakes. And with 5 people you can have 10 handshakes. In the end you'll get 10 handshakes (max) from 5 people in one group. The way to do this experiment is by getting 3-5 group members and try to handshake as many other group members as you can without handshaking a single person twice and once you reach your max, that's how many handshakes you can have. The function rule to finding out how many handshakes can take place with a certain amount of time is F(n)= n(n-1) .  
                                                                                                                                                 2

Why Math?!?

There is only math because God said so. There are many ways to think about why there is math today and one of the "doorways" to that conversation is through spiritual/philosophical thinking. In Genesis 1:28  God says "be fruitful and multiply; fill the earth and subdue it; have dominion over the fish of the sea, over the birds of the air; and over every living thing that moves on the earth." And there are many things you can take away from this, but what I took from this in a mathematical point of view is that it takes more than one (thing/person) to increase and in looking at this we see that God used a mathematical term , multiply, so as I think about how math came to be, maybe that's why/how. And in this case two people reproducing to multiply population. Another doorway is personal. And math could be helpful in many, if not all things you do, for example: Being fruitful and multiplying. And being practical there is math to help define things or help find an answer that someone might not see.