Aim: How do we solve logic problems using conditional?

Ex: If two angles are congruent then two angles are both right.
If the two angles are not congruent then two angles are not both right angles.

Converse is just switching the hypothesis and conclusion
When the conditional and the converse are both true it is called a bi conditional

Contrapositive: Contra- Prefix meaning "against or "opposite"
So you just negate and switch the hypothesis and conclusion (Inverse and Converse)
For Ex: The Contra-positive of "If i study then ill pass geometry is :If i failed Geometry, then i didn't study.

Aim: What is a mathematical statement?

A mathematical statement is a statement that can be judged to be true or false.

Ex: 17-5=12--True
The George Washington Bridge is in California--False

Negation-"Not"
Always have the opposite truth Value

And-Both statement must be true in order to be true
Or-Either statement (or both) can be true for the statement to be true

Conjunction- And,or,but

Conditional-The conditional is the most frequently used statement in the construction of an argument or in study of mathematics. (i.e geometric proofs)

 Inverse- Formed by negating the hypothesis and conclusion

4 Condional that can be formed...
The Conditional- If it is raining then it is cloudy
The Inverse-If it is not raining then it is not cloudy
The Converse-If it is cloudy then it is raining
The Contra-positive- If it is not cloudy then it is not raining

Aim:What is logic?

Logic is Thinking
Logic is the tool to determine between true or false!

Ex:We use logic everyday to Get ready, Go somewhere,Etc...

How do we graph Rotations?

Describing a rotaion or a turn
1) An angle of rotation
2) A direction (Clockwise or Counter Clockwise)
3) A center of rotation

90degrees                      180degrees                      270degrees
(A,B)--> (-B,A)             (A,B)--> (-A,-B)             (A,B)--> (B,-A)
Ex:(2,5) --> (-5,2)          Ex: (5,2)--> (-5,-2)          Ex: (5,4)--> (4,-5)

Aim:How do we graph transformations that are reflections?

Line reflection: (Flip) A transformation that creates figure which are mirror images:
Rules for a reflection in the
 X-axis (x,y)--> (x,-y)
Y-axis: (x,y)--> (-x,y)