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.
