Algebraic Proof: Blog Entry #3

Throughout this blog entry, I will be identifying some of the properties of equality and the properties of congruence and reviewing them to use and write them as algebraic proofs.

Proof uses logic, definitions, properties, and proven statements to show that a conclusion is true. When writing proofs, it’s important to give justifications to show that each step is valid. These justifications can be made by using any piece of information that can be obtain from a problem.

Solving an equation uses proof, because several properties are used to solve the equation. Using  the Properties of Equality can help prove a statement to be true.

Example:

 Segment congruence means two line segments are congruent if they have the same length.

By knowing this, we could come to the conclusion that each property of equality have their own corresponding property of congruence. Properties of equality do apply to segments as well, and also three properties of congruence does too.

Reflexive Property of Equality: Segment AB = Segment AB

Reflexive Property of Congruence: Segment AB ≅ Segment AB

Symmetric Property of Equality: If Segment AB = Segment CD, then Segment CD = Segment AB

Symmetric Property of Congruence: If Segment AB ≅ Segment CD, then Segment CD ≅ Segment AB

Transitive Property of Equality: If Segment AB = Segment CD and Segment CD = Segment EF, then Segment AB = Segment EF

Transitive Property of Congruence: If Segment AB ≅ Segment CD and Segment CD ≅ Segment EF, then Segment AB ≅ Segment EF

  From the definition of segment congruence, the properties of equality and the properties of congruence are the same. It is true since they prove to be the same to each other, and the definitions, statements, and examples of each property are the same. We were able to  prove that these properties are true for segments .

 A deductive proof uses logic and reasoning to come to a valid conclusion. A conjecture based on inductive reasoning, is a statement believed to be true based on patterns formed from multiple observations. Using deductive reasoning and inductive reasoning is different, the processes use different methods to achieve solutions.