2.2 Properties from Algebra

Yesterday, we learned about the properties from algebra. The terms are down below.
Properties of Equality:
Addition Prop.  If a=b and c=d, then a+c=b+d.
Subtraction Prop. If a=b and c=d, then a-c=b-d.
Multiplication Prop. If a=b then ca=cb.
Division Prop. If a=b AND C DOES NOT = 0, then a/c=b/c.
Substitution Prop. If a=b, then neither a or b may be substituted for the other in any equation (or inequality).
Reflexive Prop. a=a
Symmetric Prop if a=b and b=c, then a=c.
Remember that DE=FG and _  ~  _
                                           DE=FG can be used interchangeably, so can m angle D=m angle  E and
            ~
 angle D=angle E. So the following properties of congruence follow directly from the related properties of equality.
Properties of Congruene:
                          _  ~ _                        ~
Reflexive Prop. DE =DE           angle D=angle D
                               _  ~ _            _ ~  _
Symmetric Prop. If DE=FG, then FG=DE
               ~                                ~
If angle D= angle E, then angle E= angle D.
                               _  ~  _            _ ~ _          _ ~ _
Transitive Prop. If  DE= FG and FG=JK,then DE=JK.
               ~                              ~                               ~
If angle D=angle E and angle E=angle F, then angle D=angle F

The properties of equality and other properties from algebra, such as the Distributive Prop. can be used to justufy your steps when you solve an equation.
Distributive Prop. a(b+c)=ab+ac
It is possible to interchange your steps. If there is, they would eventually end at what you're trying to prove.
An example to justify your step is below.
side note:( I'm using this as an example so I don't have to spend too much time just so i can write notations which gets really annoying :) )

Statements                 Reasons
1.RP=TQ                  1.Given
   PS=QS
2.RP+PS=TQ+QS    2.Addition Prop. of Equality
3.RP+PS=RS            3.Addition Prop. of Equality
   TQ+QS=TS
4.RS=TS                   4.Substitution Prop of Equality.
We had to take these notes by ourselves so yeah...
and we got 2.2 pg 41 #11-14 for homework. The day before that we had 2.2 pg 41 #2-10.
Now I'm finally done and can get a break so before I finish, I'm gonna type everyone's name onto this and pick one at random by having my sister type out the names.
Krista, Kerry, Phillip, Matthew, Philip, Emma, David, Dmitri, Holly, J.D., Kaitlyn, Alivia, Zhara.
And the scribe is

 

 

 

 

 

 

 

 

 

 

 

 

Emma! Don't complain and get the work done.