Download M2 Geo Journal 2

Alejandro Gonzalez
M2 Algebra
Geo Journal 2
Conditional if then
statements
A conditional statement or if then statements is a
statement written in the for of if P then Q. In a
statement P is the hypothesis and Q is the
conclusion.
Ex 1: If you clean the dog then you may go to
the park.
Ex 2: If you do your homework you may go with
your friends to the movies.
Ex 3: If you eat the spinach then you may have a
candy.
Counterexamples
A counterexample is a example that says and
proves that the conjecture is wrong.
Ex 1: If you don't watch the movie then you won't
know about it. False because they might say to
you what's the movie about.
Ex 2: If you don't have a bath you will smell bad.
False because you can use deodorant.
Ex 3: If you don't put away your school materials
then you will be late tomorrow morning. False
because you can e
What is a definition?
A definition has the description or meaning of
something.
Ex 1: Carbon dioxide is the compound that
animals exhale after inhaling oxygen.
Ex 2: Wood is a material extracted from trees.
Ex 3: Coffe is drink that comes has caffeine.
Biconditional statements
A Biconditional statement is a statement that
can't be contradicted and it's written P if and only
if Q. They are used to show that the hypothesis
depends on the conclusion to determine if the
statement is valid or invalid. They are important
because they are very specific so your answer
will always be the same.
Ex 1: You get good grades if and only if you go
to school every day.
Ex 2: You have friends if and only if you talk with
people.
Ex 3: You are healthy if and only if you do
exercise.
Deductive reasoning
Deductive reasoning is when you use
observations to make a conclusion. Inductive
reasoning is when you use facts to make
conclusions.
Ex 1: They say that Lamborghini was founded
after Ferrari because of competition to see
whitch car was better. This is inductive reasoning
because it is a fact.
Ex 2: All of the music has instruments therefore
all of the instruments make music. This is
deductive reasoning because it's based on
observations.
Ex 3: Water creates moisture therefore all of the
moisture is from water. This is deductive
reasoning because it is based on observations.
laws of logic
The law of Detachment is if p then q is a true
statement and p is true then q is true.
Ex 1: If you eat less you lose weight. Rona lost
weight because she ate less.
Ex 2: If you have internet then you have a
computer. Bob has a computer with Internet.
Ex 3: If you take a bath then you smell good. You
smell good.
Law of Syllogism says that if p then q then r are
true statements then p then r are true statement.
Ex 1: You are hot then younuse A/C to cool
down. You are cold because of the A/C. You are
cold with an A/C
Ex 2: If you have a Veyron then you are a
millionaire. You have a Veyron so younger a
millionaire.
Ex 3: If an animal has hair then it's a mammal.
You have hair so you are a mammal.
Algebraic proofs using
the algebraic properties
of equality
Proofs are a way to solve problems giving
evidence of each steps to solve.
Ex 1: Subtraction property of equality, if a=b then
a-c is b-c
Ex 2: Multiplication property of equality, if a=b
then AC=bc
Ex 3: Reflexive property of equality, a=a
Two column proofs
In a two column proof you write the steps on the
left side and the reason of the steps on the right.
Linear pair postulate
(LPP)
The lPP says that two lines that form a linear
pair are supplementary
Congruent complements
theorem
The theorem says that If two angles are
complementary to the same angle then the 2
angles are congruent.
Congruent supplements
theorem
If two angles are supplementary to the same
angle then the two angles are congruent.
Vertical angles theorem
Vertical angles are congruent, the angles the
non adjacent angles will have the same
measurements
Common segments
theorem
if segment ab is congruent to segment cd then
segment ac is congruent to segment bd
Ex 1: If Chicago to Detroit is the same as
Seattle to Los Angeles then Chicago to Seattle is
the same as Detroit to Los Angeleles.
Ex 2: If Miami is the same distance to Orlando
and Tallahassee to Tampa then Miami to
Tallahassee is the same as Orlando to Tampa.
Ex 3:
Journal Finished