5.1 and 5.2

Today in class (5.1) we learned about different arguments and proving something that is a not proof.
One argument is the direct argument. Its just the general:
p  q
p
                    
  q 
Another one is the transverse argument:

p  q 

q  r

                    

 p   r 

The last is an indirect argument.

p  q 

      q

                   

  q 

We then learned about how to prove a proof such as; 

Given: AD   CB

Prove: AD does not bisect CAB

When you have a proof that has the word not in it, you take it, and you assume the opposite. So, in this case, it said that AD doesnt bisect CAB which would mean that you would start your proof saying AD does bisect CAB. If your proof contradicts itself, then the statement is true. If it doesnt, the statement of which your supposed to prove is false.

Then we learned 5.2. 

Angle 2 is the adjacent interior angle and angles A and B are the remote interior angles.  Angle BCD is the exterior angle.  We learned that all triangles have 6 exterior angles but there are only 3 different measurements of the angles. So, we know that  m1 + m2= 180 degrees. We also know that mA + mB + m2 = 180 degrees. Knowing both of those, we can get that mA + mB + m2= m1 + m2. Therefore meaning that mA + mB= m1. So, m1 is greater than mA as well as mB.  

Lastly, we learned how to prove two lines parallel.  To do so, there are 7 theorems that you can use. ( ll means parallel)
1. alt. int. s -> ll          2. alt. ext. s -> ll  
3. corro. s -> ll    4. 2 lines  same line-> ll
                          5. sup. same side int. s -> ll        6. sup. same side ext.  s -> ll
                          7. two lines ll to same line -> ll