Algebraic Proof

     Hey there! This week's topic is about algebraic proof. I am reviewing and identifying properties of equality and then using them to write algebraic proofs. A proof is an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true. 

     The definition of a segment congruence: two segments that have the same length. The reflexive property of equality corresponds to the reflexive property of congruence. It can be written as A equals A or A is congruent to A. They are the same thing.  Moving on to symmetry, the symmetric property of equality and the symmetric property of congruence are similar as well. For equality it can be written as "a=b, b=a", for property of congruence it can be written as "if a is congruent to b, then b is congruent to a". Last but not least, transitive property of equality and congruence. In transitive property of equality, you can write "1=2, 2=3, 1=3". It would mean the same thing as saying, " 1 is congruent to 2, 2 is congruent to 3, 1 is congruent to 3". They both mean the same. 

     I'm going to use the conclusion "If the first letter of the alphabet is A, then the second letter of the alphabet is B." This conclusion uses facts and patterns. Also, if this were a conjecture, you would know that the third letter of the alphabet is C. You know it's C because of the pattern and direction the blogger is going in. 

     We've actually already done proof! Can you believe it? The equations we learned to solve in 8th grade is an example of when we learned to apply proof. For example, in different equations we learn how to use distributive property and substitution property. When you justify your steps of an equation it is a way of validating and authenticating your steps. 

The pictures were taken out of my textbook. They are not mine. No copyright intended.