How do we solve logic problems using conditionals?

In the logic unit, we are not looking at one statement at a time. If "and", "or" is in a statement it is true if one is true and vice versa. Conditionals are the most frequently used statements in the construction of an argument.

Ex) 

Inverse: formed by negating the hypothesis & conclusion

  - If it is cold, then i will take my coat

  - If it is not cold, then i will not take my coat

Converse: is just switching the hypothesis and conclusion

  - If today is Friday, then tomorrow is Saturday

  - If tomorrow is Saturday, then today is Friday

Contrapositive: contra- prefix meaning "against" or "opposite"

  - If i am tired, then i will go to sleep

  - If i am not asleep, then I am not tired

Bi-conditional: when the conditional and the converse are both true

  - If my shoes are untied, then I will tie them

  - I will tie my shoes if and only if they are untied

Question:

Make a conditional using this phrase:

   If today is Monday, then yesterday was Sunday.

What is a mathematical statement?

    A mathematical statement is a statement that can be judged to be true or false. For example she is wearing a blue shirt is a mathematical statement because it can be proven true or false.

Ex.
He is holding an ax in his hand.


Questions:
Which one of these are NOT mathematical statements?
a) 3+5
b) Nobody is home
c) The dog is wagging its tail
d) 3 = 5

How do we identify composition of transformation?

Composition of Transformation- When 2 or more transformation are combined to form a new transformation, the result is called a composition of transformation.


The composition sign is the little circle between the to transformations

Guided Practice Question:
1. What is the new point (5,4) under the composition of transformation r x-axis following T (-4,6)?

How do we use the other definitions of transformation?

Glide Reflection- The combination of a reflection in a line and a translation along that line.


Isometry- A transformation of the plane that preserves the length of the sides



Orientation- orientation refers to the arrangement of points relative to one another, after a transformation has occurred

Invariant- a figure or property that remains under a transformation of the plane. No variations have occurred.

Guided Practice Questions:

1. The arrangement of points after a transformations that stay the same is an example of
   a. orientation
   b. dilation
   c. translation
   d. all of the above

 

How do we solve problems using reflections?

A reflection also called a flip show a flipped image of a geometric figure over a line of symmetry on a coordinated plane


EX: If the figure is reflected on the x-axis the y value in the point will go to its negative reciprocal.
      If the figure is reflected on the y-axis the x value in the point will go to its negative reciprocal.
  

Practice Questions:

1) If point A is plotted on coordinates (4,5) what is its reflected image over the x-axis?

1. (4,5)
2. (4,-5)
3. (-4,5)
4. (-4,-5)

How do we graph dialations?

The way you can dodialations is to multiply the dimension of the original im age by the scale factor to get the dimension of the dialated image.

Scale Factor is when the image stretches or shrinks

If the scale factor is greater than zero and less than 1 then the image will shrink.

If the scale factor is greater than 1 then the image will stretch

Ex.)

Practice Question:

 1) Perform a Dilation of ½ on point A (2, 4).

 2) What are the points of triangle ABC where A(4,3) B(6,1) C(18,4) where it was dialated by 4