Blog Entry #3

Welcome back to another blog entry! The lesson that I am learning about this week involves using properties of equality and congruence. I am learning to write justifications to prove that every step in an algebraic equation is valid. If you guessed that our lesson is about Algebraic Proof, then you were right! 

So the main purpose of this lesson is help us develop the skill of determining whether every step we make is valid using justification. Developing this skill not only will apply to geometry, but it's possible to use this skill in our everyday lives. 

What I am doing is using the definition of segment congruence and the properties of equality to show that all three properties of congruence are true for segments.

Segment congruence is when two segments have equal measures and length

Now based on the definition of segment congruence and the properties of equality, I have proved that all three properties are true for segments because it shows similar examples. Reflexive, symmetric, and transitive properties of equality and congruence have the similar examples. Therefore, segments that are congruent are equal to each other.

So now that I finished explaining the first question, I will now proceed to the second question. In this next one, I need to compare the conclusion of a deductive proof and a conjecture based on inductive reasoning.

First of all, the conclusion of a deductive proof is found through deductive reasoning, which uses actual facts to draw a conclusion. A conjecture is a statement believed to be true. Inductive reasoning is using patterns that you observe to prove that a statement is true. Based on what I observe from both the conclusion of a deductive reasoning and a conjecture based on inductive reasoning, I can conclude that both are different from each other. The conclusion of a deductive reasoning can either be true or false. If one of the statements of deductive reasoning is false or can be contradicted, then the conclusion of a deductive reasoning is wrong. The conclusion of deductive reasoning is also based on actual facts. The conjecture of inductive reasoning is based on fact pattern, not by actual facts through research. 

In conclusion, I have learned a lot from this lesson. Algebraic proof helped me learn more about deductive and inductive reasoning. And because of this, I have developed to use reasoning skills that I can use in my everyday life.